No. I don’t think UMich will match scholarships, but it certainly isn’t going to match the instate tuition of another school. If UMich wants to give you a scholarship or other FA, it will, but it won’t do it because Wisconsin would only cost you $40k. GaTech give very little FA to OOS students unless you win a Stamps or other named scholarship.
I think you can approach the school and say it is your first choice but financially not going to work. You can show them the other offers, but usually the big flagships aren’t going to match anything. Might come up with a small department scholarship but not going to get you $20k. I also don’t think UMich cares what Mich State is offering or GaTech is going to match any UGA offers.