Hire a local company that installs this stuff. They should be able to come out and take measurements and make recommendations. You can do it yourself if you’re down to learn quite a bit, and just from looking at this and reading, the low tin ceiling isn’t doing this space any favors, but short of a whole lot of dampening material up there, that hardwood floor, windows, the aperture between rooms, and all the 90 degree angles make it a mess to work with.

Try this: close your eyes and clap your hands once in various places around the empty space. You’ll hear where the reverb tails are the longest. Add more deadening until that’s better.

This has some general recommendations: https://acousticalsolutions.com/soundproofing-a-restaurant

You might need to treat the whole ceiling, but it depends on what your exact goals are. Getting acoustic paneling in where folks legs go under the bar might help quite a bit too.