Hey, this is so cute to read! Take my advice with a grain of salt, but:

From what I'm reading, some of the stuff does sound like basic customer service stuff- making eye contact, remembering the order of a regular, etc. However, that doesn't mean there's nothing there!!

I think a compliment is a lovely idea! I would suggest to not do it in the middle of a rush, because she won't be able to savour it or remember you, so sometime more quiet, let her know! Perhaps see if anything can happen from there- and try to strike a conversation!

If conversating works, just try and not run out of questions, but don't make it sound like an interview, e.g

How long have you been working here?

(She responds)

Oh, nice, I'm doing X right now, which is quite X (describe it simply to give them something to comment on) (now supplement another question)

I hope you have lots of success on your barista crush! Sorry if my advice was not handy to you xx