There's a lot to unpack here, and others including /u/NewtownianassPounder have made a good start, but I just wanted to engage with a very specific problem we occasionally see in posts like this.

The problem is, there's some retro-fitting of history at play here; "Ireland's population is small now, so why was it larger then?"

Historically, Ireland was the second most fertile and second most populous region of these isles by a considerable distance. Unlike Scotland and Wales, which were overwhelmingly mountainous, Ireland was a country of low hills, meadows and farmlands, just as England was. For comparison to the countries you listed, Egypt is 96% desert. Austria is 60% high mountain. Likewise 60% of Scotland is covered by highlands. The US, while extremely fertile, wasn't even 50 years old. Ireland did not have any of these problems - much like England it was a country of low hills, meadows and farmlands and was extremely arable. As we can see from a glance, England's population for the period was about 15 million, significantly higher than any of the countries you listed. France, for example, had many times more again at about 35 million for the period. In fact, rather than what your question suggests, Ireland's population size was bang on the money for a largely arable country that was undergoing industrialization. In fact, we have several examples of less-arable countries which adopted industrialization later than Ireland but which maintained their population growth and whose modern day populations are significantly higher.

Generally speaking, the more important question is "why did Ireland's population decline?" And unless one subscribes to Trevelyanism, that is a very complex question which essentially boils down to a truly historic case of state mismanagement, intentional or otherwise, which the country has never recovered from. Had the British state not enacted generations of anti-Irish policy leading to the inevitability of the human catastrophe that was the famine and the decades of withering that came after it, it's hard to see how Ireland isn't a significantly more populous country today.

Edit: I've commented a better answer here, please ignore the below.

The adoption of the potato and growth of population was more of a symptom of the landholding system enforced by the British over Ireland, where by the eighteenth century it’s estimated that Irish land ownership was around 5%, the rest owned by Protestant, often absentee, landlords.

Taking from ‘Atlas of the Irish Famine’ (a compendium of various contributors), William J. Smyth describes how the potato allowed the colonisation of poorer land and facilitated the population growth, along with the growing textile industry and the spread of smallpox inoculation. In the decades before the Famine, the Irish poor were described as handsome, athletic, and robust, nourished by a diet of potatoes and milk, and warmed by a plentiful supply of turf, as a result the life expectancy of the Irish was equal if not greater than other Europeans.

John Feehan details the increasing reliance on the potato due to two parliamentary acts; the Act to Encourage the Reclaiming of Unprofitable Bogs (1742), and the Catholic Relief Act (1793). The former allowed for Catholics to lease fifty acres of bog along with one half acre of arable land, in return they would be free from taxation for the first seven years after reclamation. The latter gave elective franchise to Catholics who were ‘forty-shilling freeholders’, this encouraged landlords to lease marginal land and increase the number of freeholders they had on their land to increase the number of votes they controlled. The forty-shilling threshold was withdrawn with the Relief Bill of 1829 but the tenants kept their land. The extensive bog reclamation during this period would not have been possible without the potato.

David Nally as part of his contribution describes the British colonial dimension that led to the large population growth. The Irish economy had been reconfigured to supply the food needs of England, and as the Irish population increased so too did the dependency on the potato and competition for land not being used for cash crops. Further exasperating the situation was that there was no legal restraint on tenants subletting their land to the point where estates were subdivided into barely viable smallholdings. As competition for land grew Irish labourers often had to bid higher rents for smaller slips of land, to the point where most their time was spent trying to meet rent rather than nutritional needs.

(Sorry this was a bit of a quick answer, I’m short on time but couldn’t resist answering)

Replying specifically to your question, "Why was Ireland so populous (at this time)?", I'd point you to Ó Gráda, who is arguably the foremost scholar of the socioeconomic aspects of Famine-Era and immediately pre-Famine Ireland.

Ó Gráda points out that the population bump in the early 19thC is of course complex and multivariate (it's never just about the potato), but identifies 3 primary factors that contributed specifically to the Irish case:

Precocious marriage, high fertility rates, and decreased mortality.

The first two are obvious, but worth pointing out that Irish tradition encouraged marriage relatively earlier than other cultures in Western Europe at this time - often at menarche or soon after for women.

It's the declining mortality, however, that factors in particularly at this time - and again this is due to several advances. Yes, the prevalence of the potato and buttermilk meant that even the peasant/labouring class enjoyed a diet with high caloric density and vitamin profile. (Nicolas & Steckel) Also important was the wave of "proto-industrialization" taking root in parts of the country - primarily textiles in the northeast (what would become NI) and Dublin. These were trends elsewhere in Europe, but the combined effect on population in Ireland was particularly pronounced.

See: Ó Gráda, Cormac (1979). "The population of Ireland 1700-1900 : a survey". Annales de Démographie Historique, 281-299.

Nicolas & Steckel (1992).Working Papers "Tall But Poor: Nutrition, Health, and Living Standards in Pre-Famine Ireland." National Bureau of Economic Research Working Paper 39.

Almquist, Eric. (1979). "Pre-Famine Ireland and the Theory of European Proto-industrialization: Evidence from the 1841 Census." The Journal of Economic History 39: 3, 699-718.

(Edited to format citations)

The proliferation of the potato was certainly a central factor in the rapid increase of Ireland’s population, but it only goes so far to explain as to why this happened in Ireland, what other factors contributed to the population growth, and what made the potato so “popular”.

In the 18th century, the potato had established itself in the Irish diet in tandem with oats; potatoes would be consumed with buttermilk from August to March until the oat crop would be harvested. This would change by the end of the century when increasing cereal prices meant grown oats were instead used to maximise cash income, and the development of new potato varieties that could hold all year meant that the Irish diet trended toward a potato monoculture. Due to the high calorie diet provided by potatoes and milk, and in part due the significance of smallpox inoculation, the Irish life expectancy grew to be better than most European countries.

However, the adoption and later dependency of the potato could also be seen as a symptom of the landholding system enforced by the British over Ireland. Through conquest and colonisation in the prior centuries the Irish economy had been reconfigured to supply the food needs of England, and by the 18th century it’s estimated that Irish land ownership was around 5% while the rest of the most arable land was owned by Protestant, often absentee, landlords.

The labourers or cottiers who worked the land of these landlords were often provided with a piece of land, a “conacre”, to grow their own food in lieu of wages. The population growth in this “cottier underclass” was the most significant in Ireland, provided by the previously mentioned increase in life expectancy but also by couples getting married younger and having more children. As demand for land increased with the growing population, the conacre plots would become smaller and marginal land such as bogs and steep hillsides would become utilised. This was only possible as the potato could grow in soils unsuitable for other crops and had a significant calorie to land use ratio i.e., a high number of calories for a small plot of land.

Two parliamentary acts would encourage this subdivision and marginal land use; the Act to Encourage the Reclaiming of Unprofitable Bogs (1742), and the Catholic Relief Act (1793). The former allowed for Catholics to lease fifty acres of bog along with one half acre of arable land, and in return they would be free from taxation for the first seven years after reclamation. The latter gave elective franchise to Catholics who were ‘forty-shilling freeholders’, but this would only encourage landlords to lease marginal land and increase the number of freeholders they had on their land to increase the number of votes they controlled. The forty-shilling threshold would be withdrawn with the Relief Bill of 1829 but the tenants kept their land.

Further exasperating the situation was that there was no legal restraint on tenants subletting their land to the point where estates were subdivided into barely viable smallholdings. As competition for land grew Irish labourers often had to bid higher rents for smaller slips of land, to the point where most their time was spent trying to meet rent rather than nutritional needs.

I do note that much of what was stated does go beyond 1821, as said the population of Ireland was 6.8 million at that time, but it would peak at 8.5 million on the eve of the Great Famine in 1840. At this point it’s estimated the agricultural output of Ireland could feed 9.5 – 10 million, the 8.5 million in Ireland and the rest exported to England in the form of grain and livestock. It sounds contradictory where previously mentioned that Ireland was supplying the food needs of England, but it does show the precariously reliance on the potato monoculture and how once it collapsed that Ireland would not recover to the same population even into the modern day.

Sources:

Various, Atlas of the Great Irish Famine, Cork University Press, 2012

Various, Famine 150 Commemorative Lecture Series, Teagasc, 1997

C. Ó Gráda, “The Population of Ireland 1700-1900: A Survey, Annales de démographie historique, 1979