Choose 'changed legal residence in 2021 to WI and wasn't a resident of WI any previous year'.
It's interesting that Wisconsin is asking so many questions! Most states simply ask for the dates you moved in/out of the state. Do the best you can answering these; the net out being that you were a part-year resident for four months (and a part-year resident of IL for 8 months).
To figure state taxes owed, many states take your total income from your Federal return and calculate a % of it as being earned in that state, based on the number of months you lived there.
However, other states ask you to split out your income between their state and the 'other state' (this info hopefully being on your W-2 so no calculations are required by you), so don't despair if the calculations on the state returns seem odd.
It's also interesting that your employer withheld both Illinois and Wisconsin tax on your pay, since they are 'reciprocal states'. Enter your W-2 as it is shown, and the state returns in TurboTax will sort it out.
Click this link for more info if you're interested.
Don't worry about the address on your W-2; the current address for a taxpayer may not be in any of the states they worked in! The IRS only needs to know where you are now.
This link has more info on preparing a Part-Year Resident Return.
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