Actually, it IS an add back on the IL side. See the 2021 IL-1120-ST instructions, page 8 of 31:

You must add back any amount of Illinois Replacement
taxes and surcharge that you deducted on your federal Form 1120S
to arrive at your ordinary business income. You are not required to
add back taxes from other states taken as a federal deduction.
An S corporation that elects to pay PTE tax must add back the
amount of that tax deducted federally, in addition to the add back for
replacement tax deducted.