Less than 40,000

One would hope with 5x fewer people!

I think it’s far fewer, probably under 5,000 if we are really talking about “bars” and not any ole liquor licensed establishment such as a restaurant…

It seems like you're pretty close with that guess.

https://www.ibisworld.com/us/industry/ohio/bars-nightclubs/1... (2025) estimates there are about 3,000 "bars and nightclubs" in Ohio.

And https://vinepair.com/articles/map-states-with-most-bars/ (2022) estimates there are 1800 bars in Ohio, apparently placing it in the Top 10 of states with the most bars.