Will I need to change my federal allowances if my tax bracket changed?

what new tax rules are you referring to? other than an adjustment for inflation, the tax brackets are the same in 2022 as they were in 2021.  

if you are referring to your withholding on your paycheck, see you payroll department and adjust Form W-4, if necessary.    

IRS issued new calculations.

Your employer should take care of that for you automatically.

This is supposed to increase your probability of a refund, not increase your tax bracket.

@mhachmann