Ariel, it is not a strict uniform, just the local costume.
And not specific to zeybeks either. This is mostly similar to most town folk wore in Ottoman Anatolia and Balkans in 19th century.
And that so-called "Zeybek" yatagan with T shaped ears. That is not specific to zeybeks either. It is just easier to make than a real ear shaped handle. And in late 19th century-early 20th century small town blacksmiths were not expert swordsmiths like in earlier times, so most made those ears T shaped because it was easier to make. Some yatagans that were made earlier also got those T shaped pommels when their original fancy handles got fallen apart and their owners or the local knifesmith made these simple handles for them.
Zeybek yatagan is just a name given by contemporary antique dealers, just to make it easier to classify and make it sound more important.