Yes you should. Will it be on your W2 or will he give you a 1099 for it? Here are the blank Estimates and instructions (the actual 1040ES forms are at the very bottom so scroll way down)
Or You can pay directly on the IRS website https://www.irs.gov/payments
Be sure to pick the right kind of payment and year.....2022 Estimate
Typically, yes. How it's taxed depends on if it's a true "bonus" payment, and/or if it will be included in box 1 of your W-2 when issued. Typically, if you send the IRS 20%, you'll be fine at taxing filing time. If you state taxes personal income, you'll probably need to pay estimated state taxes too.
Any payment from your employer, no matter what the employer calls it or what reason they give for it, is supposed to be treated as wages and included in the wages on your W-2. If the bonus is not included in your W-2 at the end of the year, or if your employer gives you a Form 1099-NEC or 1099-MISC for the bonus, check back here when you are working on your 2022 tax return for instructions on how to enter it in TurboTax so that you don't get stuck paying more tax than you should.