As to "why" people converted, this is a complex question. It's related to the relative strength of the pre-existing faith communities, winning political or economic favours, or how comfortable the Ottomans were with regional autonomy in areas which were seen as strategically important. And even then, many Christian Albanians choose to leave than convert, which is not the same thing as the population of Albanians widely converting to Islam, even if the percentage of Muslims in Albania subsequently increased. And, even today, mind you, there are plenty of Catholics in Albania.

But I want to turn your question on its head. The reality is, many people in Greece did "embrace" Islam, as much as a colonized people could "embrace" their colonizer's religion. Take a look at this painting of Athens during Ottoman rule from 1800:

https://upload.wikimedia.org/wikipedia/commons/7/75/Bazar_of_Athens.jpg

Which is to say, there were plenty of Muslims in what is today Greece.

This leads to the more complex issue of religion and culture in the Ottoman Empire. Compared to their contemporaries in Catholic Europe, the Ottomans tended to be much more tolerant of Christians, Jews, and even pagan religions like that of the Yazidis. This is rather significant since Western Europe totally wiped out its pagan and Muslim populations, and when you get down to it, didn't stop trying to exterminate the Jews until the mid-20th century. As such, even as an oppressed minority religion, Greek Orthodox Christianity persisted in the Ottoman Empire in a way that is quite cosmopolitan by early modern European standards.

Moreover, the Ottoman heartland was, of course, also the heartland of the former Greek-speaking Byzantine Empire. Aside from relative tolerance of Greek Christians, the Ottomans, like most pre/early-modern states, were much more comfortable with the idea of minority languages which ran across ethnic, regional, class, or religious lines compared to the modern nation-states we live in today, where nationalists lose their shit over having to "dial 1 for English". Greek speakers rubbing shoulders with Turkish speakers rubbing shoulders with Arabic speakers in the same city was the rule, not the exception.

In all of this, I'm stressing that the area that what became Turkey had a lot of people we would now consider "Greeks" living in it, and Greece had a lot of people we would consider "Turks" living in it, and lines between them weren't so clear-cut as we might imagine with Greeks and Turks at each other's throats today. There were all sorts of people who didn't fit the bill as one ethnicity or another. A Greek-speaking Muslim named Spiro that moved to Ottoman Iraq and married into an Arab family is a... what?

With the post-French Revolutionary explosion of nationalist movements throughout Europe, and with the help of western Europe's push into Ottoman lands in the 19th century, Greek-speaking Christian people began to see themselves as a distinct nation which deserved sovereignty. And as the idea of a Greek (and throughout the next century, Turkish) nation developed, there was more and more of a push for national uniformity-- a national culture, national language, and national religion, with less and less room for ethnic ambiguities like Spiro the Muslim Greek in Iraq. But it wasn't until a century after the War of Independence started, in the aftermath of the Greco-Turkish War of 1919–1922, that there was a large-scale population transfer of Greek Muslims who were moved to Turkey and Greek-speaking Orthodox Turks who were moved to Greece. We see this process play out still today in Cyprus, which, as you may know, is an independent country with large Turkish and Greek speaking Muslim/Christian populations. This became the site of a irredentist struggle where Greece tried to annex the independent country on the pretext of there being a population of what we could now consider "ethnic Greeks". They had never been part of a Greek state, but they were claimed by Greece as part of the Greek nation. Similarly, Turkey tried to protect "their" population of "ethnic Turks" by invading the island.

This continues today:

https://en.wikipedia.org/wiki/Cyprus#/media/File:Cy-map.png

And you can probably imagine that people didn't live on opposite sides of the island with a demilitarized zone in the middle 200 years ago.

To sum up, Ottoman "Greece" was not exactly "Greek" and Ottoman "Turkey" was not exactly Turkish: there was a much larger diversity of cultural practices and regional beliefs than in either modern nation state.

And all of this applies to the former Yugoslavia, which was, as, a post-Ottoman state, an ethno-religious melting pot that was violently torn apart by ethno-linguistic-religious nationalist movements. And, maybe someone that knows a lot about Albanian history can go into this, but I would strongly suspect the exact same thing played out in Albania.

Edit: I should add, things were far from rosy for people who followed minority religions in the Ottoman Empire, but I'd rather be a Christian in 15th century Istanbul than a Muslim in 15th century Toledo any day of the week.

Edit 2: And the more I think about it, the question of why people convert to a new religion as individuals (in a country where power relations between their community and that of the dominant group are totally unbalanced) is an extremely complex one. For an individual, it may have been a situation where they felt compelled to because other people in their family or local community were converting. It may have been because they wanted an administrative job, or had other financial incentives. It may have been that many people were genuinely moved to convert. But it may also have been because of how Islam and Christianity were imagined in discourses present in the Ottoman Empire at the time. One might have felt more powerful or elite becoming a Muslim than they were as a member of a disprivileged minority religion whether they gained anything materially or not. It's impossible to answer this question definitively, I think, based on so many factors.

Edit 3: So many grammar mistakes. Never post in the middle of the night.