uneeq: “You would have to prove that the issur also applies to other things aside for bread”
First of all, bourekas are bread. Secondly, the Tzemach Tzedek who applied Ein Mevatlin was discussin wine and the Taz forbids a spice grinder, clearly not bread foods. The bottom line according to their opinion is that anything eaten with both meat and dairy must remain pareve, and this would apply to bourekas as well.
“This doesn’t apply to borakas unless you can prove that borekas are eaten with (directly, it’s not enough in the same meal) meat and dairy.”
In EY they are commonly easten as a side dish with the main course, which could easily be meat.