I made a mistake on my 2021 Ohio State tax return and as a result had to pay $450 in taxes in 2024. Can I get a credit for those?

Are you itemizing deductions for your 2024 tax return?  Are you entering mortgage interest, property tax paid, medical expenses, etc.?    And was the $450 all tax --or was some of it a penalty or interest?

If you paid taxes due in 2024 to your state or local government, you can enter that by going to Federal> Deductions and Credits> Estimates and Other Taxes Paid>Other Income Taxes.  You can enter the taxes you paid, but do not include any penalties or interest.

No credit but a possible deduction, if you itemize. State and local taxes are capped at $10,000 when you itemize so you may not be able to use it. As stated by xmasbaby0, it is only the taxes and only if you itemize. You can always enter the tax amount as given above. If you take the standard deduction, the program will know not to include it.