You're not really doing anything wrong.
For one thing, most employees need to complete a Federal Form W-4, but not everyone needs to complete a state Form W-4. In addition, a Federal Form W-4 tells you how much Federal income tax to withhold from each employee's pay. A state Form W-4 tells you how much state income tax to withhold. This is 1 option.
If your income is about the same year over year you could simply divide the tax you owed to the state n 2022 and divide that by the numbers of paycheck left in the year. You could then set up estimated payments for the state in 2023. Then you want to remember how much you paid so you can indicate that you paid estimated taxes for 2023 when you prepare your 2023 return.
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