I know I have to use schedule a to itemize the state tax paid in 2022 but where do I input it while being guided through the form on Turbo Tax?

There is a question for state and local income tax in the interview.

If you reported your W-2 in the program with state income taxes withheld, that amount is automatically entered on Schedule A as an itemized deduction.

To enter state income taxes paid -

Click on Federal Taxes (Personal using Home and Business)
Click on Deductions and Credits
Click on I'll choose what I work on (if shown)
Scroll down to Estimates and Other Taxes Paid
On Other Income Taxes, click on the start or update button
On the next screen scroll down to Other Income Taxes Paid in 2022

Or enter state taxes paid in the Search box located in the upper right of the program screen. Click on Jump to state taxes paid

And you don't double enter any $$ that you already entered as part of your other form entries...like your W-2 or 1099-R forms.  You just enter the state taxes you paid separately.

.....like for a balance due you paid (during 2022) for your 2021 state tax filing.

...or for 2022 quarterly estimated tax payments you made outside of TTX.

.......or if you filed a 2022 state extension, and paid some 2022 taxes at that time.