You might be confusing Pay Period and Pay Date. Also, Cash or Accrual Payroll.

The Pay Date in 2021 that is for time worked (pay period) of 2020 still is 2021 payroll. An Accrual Entity will accrue that, and that means the amount is offset by the time you get to year end for the next round of accrual.

You mention you are Cash Basis, so nothing about what you explained even applies to you.

About the only time it matters is if someone wants Bonus paychecks in the same year that they consider it earned, or they need a final paycheck to be able to include taxable fringe benefits, shareholder health, etc, on the year's W2. They might do one extra check run, for these reasons.