Edit: 24h later, and one thing has become clear to me by the votes and comments this post has generated: Like the Israel-Palestine conflict or the history of anti-Black racism in America, Ireland's colonial relationship with England is a hornet's nest of a subject. Have anything to do with it, and expect to get stung. Attempting to distance oneself from the issues surrounding it and discuss it objectively and dispassionately only makes one look heartless and ignorant, in the eyes of people whose lives are still very much affected by these historical events.
To put my cards on the table, I'm an American with both Scottish and Irish ancestry, who has never set foot in either country. But I have traveled extensively, and met a fair number of people from both. My working hypothesis is that it ultimately comes down to Scotland sharing a land border with England, and Ireland being a separate island.
From what I can gather, Scotland was an early and relatively enthusiastic adopter of the Reformation, the Enlightenment, and the Industrial Revolution. Scotland modernized not long after England and Germany did. By contrast, the Reformation never reached Ireland, industrial development wasn't complete until the latter half of the 20th century, and how thoroughly Enlightenment values ever permeated Irish culture pre-EU is debatable.
I don't mean to belittle the significant friction the Scottish have always had with their world military superpower neighbors the English. But reading historical literature from the Age of Exploration on, it's clear to me that the English and their diaspora populations held the Scottish in much higher regard than they held the Irish. While their descriptions and depictions of Scottish people were not always kind, I don't see the same level of dehumanizing racism against Irish people that was until recently fairly common among ethnically English (and to a lesser degree, Scottish!) people in Anglophone countries. Not surprisingly then, Scottish immigrants tended to integrate and assimilate into the world's "Anglo" populations quicker, with less resistance, and more completely, than Irish immigrants.
From my readings on human migration and cultural dispersal, I have the sense that Scotland enjoys a noticeably greater cultural and genetic continuity with England than Ireland does. The transition from northern England to the Scottish lowlands doesn't involve any abrupt changes in how locals talk, look, and behave. The transition to the more Ireland-like Scottish Highlands similarly happens along a smooth cline, as one travels northwest. I don't think the same can be said for Ireland. A person from anywhere in England, traveling to any place in Ireland, will be immediately aware that he is among a different nation of people. Scotland's geographic situation, then, is much more conducive to low-resistance cultural influence from England, as well as movement of people between the two countries.
If I may put it crudely, it seems as though Scotland's relationship to England was like that of a slightly backwater but integral part of the motherland, while Ireland's relationship to England was more like an overseas colony, whose natives were distinct from, far beneath, and not able to be integrated with the colonizers.
Seems a very subjective question that will have economic historians going to war. But I think not too controversial to sum up as...
One was the british empire, the other was a colony of the british empire.
Your text doesn't suggest that distinction is clear. Scotland was never conquered. Perhaps a little more negatively for the long term attitudes in Scotland, it was sold into the union by its bankrupt nobles after the Darien scheme. It has largely retained its independence as a lesser equal in the union. Ireland was indeed very much conquered, where the land was taken and the natives forced to live on as tenants during the several waves of the Irish Plantations. It was essentially ran for-profit of the anglo aristocracy.
Also, describing Scotland as a backwater of the union is unfair. The scottish enlightenment as I assumed you were referring to, added intellectual heavy weights like Adam Smith. Leaders in banking etc. Plenty of Scots became incredibly wealthy in the empire and were among the richest in the UK. People like William Jardine and James Matheson who made their fortune thanks to the opium trade. Or the slave trading scottish father of the Prime Minister William Gladstone who received the largest payout from the state to compensate for lost "property" when slavery was banned (53 million in today's pounds).
In terms of the US, it would be equivalent to asking why the South was less modernised than the North. Probably, from (majority of?) economic historians point of view, because slavery means those in power, like most oppressors, are personally better served by keeping the status quo rather than having progress. Oppressive regimes are not known as centers of creativity.
I'm sure you're aware Ireland is Catholic, but maybe not aware of the degree to which the UK had anti-Catholic laws (technically anti non-anglican laws, but again part of the union was that Scotland would be independent in religion). Those fighting for Catholic emancipation were contemporaries and indeed allies of those fighting to ban slavery. So if the question is why did Ireland not produce a James Watt say, well it did in Robert Boyle. But such people were only going to be those who would have access to education or opportunities. And that would be the minority anglo/protestant elite. That's not to discount Scotland, which had a strong cultural focus on education and had 5 universities at a time england only had 2. But that's because it was run as a 'normal' country, with expectations of benefits for the many rather than the elite.
Now it might be a question why Irish people didn't give up their Catholicism as a price of admission to further advancement in life. Without any research having been done on this, I would guess it was less to do with religion per se and more to do with sense of identity (if someone showed up tomorrow in your US town and told you to accept supreme leader Ali Khamenei of Iran as your new religious leader then you'd probably not find it acceptable, irrespective of your attitudes to islam).
how thoroughly Enlightenment values ever permeated Irish culture pre-EU is debatable
That seems borderline anti-Irish. Not that you couldn't question how much enlightenment values permeated Irish culture but you can say the same thing about any culture including the modern US. I would say the majority of people today, including those who waffle "facts don't care about your feelings", are decidedly not very enlightened when it comes to accepting science and reason over their own biases.
I would argue the difference between Ireland and the US is that the 1775 US rebellion succeeded and the 1798 Irish rebellion was defeated. Both rebellions were based on enlightenment values, guaranteeing religious freedoms and saw Presbyterian Scotch-Irish and Irish united for the last time. The Irish state that arrived 120 years later was then also based on those enlightenment values.
So if you ask, why did enlightenment values not arrive before independence. Well, it's because the imperial power explicitly prevented them. The idea that empires "advance" their colonies is obviously something imperial apologists are keen to emphasis, but something the increasing numbers of historians from ex colonies are equally keen to refute.
As for post independence, I would sum it up as poor societies don't express enlightenment values. That something that's only done after sufficient accumulation of wealth in a society to afford funding them. And ex-colonies are by definition poor. They don't have the accumulation of capital over generations and indeed are often in the position of still buying back their resources from agents of the former colonizer. This was indeed the case in Ireland and would lead to the Anglo-Irish trade war in the 1930s which destroyed the economy of Ireland.
Added to this, Ireland followed a closed semi socialist model that with the ease of hindsight seems to be a very inefficient model that sustains poverty. But that ended in the 1950s with the economic programs of Lemass. That was before joining the EEC in 1973.
So really, I think you're correlating the normalisation of a country post independence which happens over generations with concurrent events which help but aren't so relevant.