Yes.

Isn't that exactly the action of post-Perestroika, now-democratic Bulgaria?

No. This was done under communist rule, as outlined in the Wikipedia page. Many Bulgarian ethnic Turks were able to return after the fall of communism as is mentioned there as well. A political party representing ethnic minority interests was one of the first formed after the end of communist rule. It remains significant part of the Bulgarian political landscape to this day - https://en.wikipedia.org/wiki/Movement_for_Rights_and_Freedo...