I'm no expert, and have never lived in Illinois.
The instructions for the apparently relevant line (line 5 of IL-1040) state:
"Enter the amount of federally taxed Social Security and retirement income included in your adjusted gross income on Form IL-1040, Line 1 that you received from
• qualified employee benefit plans (including railroad retirement and 401(K) plans) and Individual Retirement Accounts or self employed retirement plans reported on federal Form 1040 or 1040-SR, Line 4b and 4d."
page 7 of https://www2.illinois.gov/rev/forms/...1040-instr.pdf
When you have an inherited IRA, it is an IRA (duh). So according to the description given above I would exclude it on line 5.
If I were actually in your shoes, I would probably dig into the Illinois state statutes to see if there is any better description. In my state I would not expect there to be, having done this sort of exercise before on a similar type of question.