Not really. Right/Left labeling is silly in general so it's hard to explain in those terms, but Turkish military is and has been anything but Left. You could maybe call them reformist, secular authoritarians, in opposition of religious, populist authoritarians.

Interestingly after 50 years and 2.5 coups, the kind of people they pushed out are the ones running the country for the past 20 years and they're stronger than ever. I take it as a signal that the problem wasn't specific individuals and parties, but they were merely symptoms of deeper problems with the Turkish people.

Maybe it's the same for US as well.

The left will throw them down even faster. I'm honestly baffled as to why any police bothered stopping January 6th - it predictably got them hated by the right, but they never got any thanks or appreciation from the left either, so it looks like a complete losing move to me.