Ideas
What has changed is my sim can now always select the order drink/food interactions when the bartender is present. What hasn't changed is that the bartender doesn't respond and continues to do bar tricks until the action falls out of the queue. IMHO you need to completely remove those idle flair animations and have them simply stand there ready to work. Its not realistic for them to throw bottles around continuously like that anyway.
I did another test removing my mod folder again, clearing cache, starting a brand new save. I immediately took my sim to the Rattlesnake bar in Oasis Springs (which has the large professional bar).
I got the order drink interaction. The first one queued, then failed out of the queue with nothing happening. The second time I actually got a drink (hazzah!) but when I did the order drink/food interactions disappeared from the bar. This repeated...I sometimes could order a drink and I got it, but the interaction was gone for a period of time after.
Not one single NPC sim that came in got a drink. There was a lot of hand waving to order, chatter between them and the bartender, and the bottle flair animations but not once did they serve an NPC a drink. During times when these animations were going on order drink was not available for my sim as if the bar was not being tended.
I loaded into my regular save (with the mod folder gone) and loaded up an NPC household I have never played (to avoid missing items or anything I have done in gameplay with that Sims being a factor). I went to the same bar. I got the interactions for ordering drinks and it seemed like my order was taken, but my sim was never served a drink. I never saw any of the NPC sims get a drink either. This makes me think that whatever the change was it doesn't filter into existing saves properly.
So for me its a partial fix. Yes, I do sometimes get a drink now (in a brand new save), but no, its not consistent or complete enough to be considered fixed so that bars are fully functional.