There are plenty of tax estimators out there, run a couple with your estimated income and decide if you want to consider getting married this year for tax benefits. Keep in mind that this "paper marriage" is an actual legal marriage, and will affect more than your taxes.

If you are married on 12/31/2022, then you will file as married for 2022. Taxes aren't levied on a per paycheck basis. If you want to change how much is withheld from your paycheck you will need to fill out a new W4 and give it to your employer.