I accepted a job offer in my company starting Sept 23 in TX, but did not didn't move from IL to TX until Feb 24. I paid IL state tax for Jan + Feb 24 - what do I do?

You will need to file as a part-year resident for Illinois for the period of time you still lived there in 2024.  Even if you were working in Texas, you didn't become a Texas resident until your move date.  

@brendan-pullen3 you paid state tax based on where you work and then where you live.  The state where you live gives you a tax credit for any tax paid in the state where you work.

So in this case, TX does not have state income tax, so the money you earned in Jan/ Feb is taxed by the state where you live and there is no credit for the state where you work. 

Complete a part year Illinois tax return and report the income earned in Jan and Feb,