In England it would not be unusual to walk into a quiet bar and greet the bartender with something like "hello my friend" or more informally "hello mate". Of course if it were a busy bar, you would be more concerned with ordering beer than greeting the bartender

What is the usual way to do this in Türkiye?
Would merhaba arkadaşım be to informal???

Depends on what you mean as formal/informal.

For example, when you go into an office, and the people in it are not who you meet/know, then you dont say them: merhaba arkadaşım or something like that Maybe merhaba is an acceptable greeting but iyi günler is more formal. When you go into a bar, i think you can say everything you want, because there is not an office and doesnt need to be heard a formal greeting. I think a bar (pub right?) is also informal enough

I'm thinking about when I first arrive in Türkiye......we have a journey by minibus and arrive at the hotel and within minutes of getting off the bus I will be heading to the hotel bar

How should I greet the bartender who I know from being there last year - how would the greeting be different if it is someone else who I do not know at all?

Bod, did you ever notice how so many of your requests for help are based around eating, drinking or cavorting with bar staff?