I don't use Basic nor do I prepare Ohio returns, that said,   have you looked at the Estimated Tax Worksheet for Ohio for the option like there is in Federal ?   Does Ohio offer electronic payment of balance due for the state return, if no, then most likely it won't offer that for estimates.

What about using the Ohio state website to schedule the estimate payments?   

Maybe @Jim-from-Ohio  can help.  

I use Professional and for the balance due, say for a 2022 Ohio return, a debit can be used to pay that but there is not an option in the program to pay estimated taxes for Ohio through the program.