Worked and lived in Wisconsin for 2 and 1/2 months for summer internship. Resident of Indiana (full-time student). Do I need to file Wisconsin return?

Maybe, but even if you are not required to file, you may want to file a nonresident return to get a refund of tax withholding.   

You are a resident of IN for all of 2023 - temporary absences for work or school are considered time at home (resident state).   Tell TurboTax that you earned income in another state when you set up your personal information.   After you enter all of your federal information.   Go through the Wisconsin nonresident return first and then go through your Indiana return.   If there is no refund or no tax due, do not file the state return.   

How to enter information in the personal section if you earned money outside of your resident state

If you are a nonresident or part-year resident of Wisconsin and your Wisconsin gross income (or the combined gross income of you and your spouse) is $2,000 or more, you must file a Form 1NPR, Nonresident and Part-Year Resident Income Tax Return.