Wolves:
Moving off KAT allows them to free up some cap space long term, with Lauri's extension likely being at a lower number (though not significantly) than KAT's is. It also keeps them firmly in a win now state. The draft pick back from Utah is unlikely, although I think MN would at least try to negotiate it in. If Utah prefers to send a different next-year expiring contract, say John Collins instead, that can be figured out in the cap. MN benefits from trading with two salary rich teams greatly.
Starters: Mike, ANT, Jaden, Lauri, Rudy Bench: Naz, NAW, Rob, Clarkson, Young developmental guy (Minnot, Shannon, Miller)
Spurs
Spurs trade a lot of assets, though in this case, mostly other teams' picks, and go for a real all-star, who fits well next to Wemby. SA is really building something, with Castle, Vassell, Schohan, KJ, CP3 and Tre playing PG, and now KAT and Wemby, a pairing that should work even better than the Rudy-KAT pairing was. The big question lies in: why go KAT instead of Lauri? KAT feels like a better player for the most part, and although he's more expensive, Lauri's new contract will be pretty close to KAT's anyways. I thought I heard on a podcast that Lauri is eligible for 4 years, $116, but that feels really low. I assumed it would be 4 years, $200+. It's likely closer to the second number, so with close numbers, and a slight edge on talent to KAT, Spurs go with KAT on a huge offer to Utah. Picks can be changed, but the biggest value would be the ATL 2025 first rounder, with how good that draft appears to be.
Starters: CP3/Tre, Vassell/KD, Schohan, KAT, Wemby Bench: Tre/CP3, Vassell/KD, Castle
Jazz
Utah gets the Bridges level offer they are looking for, diving deep into a full rebuild. Picks, and even players can be adjusted slightly, depending on how much Utah wants, but they prepare themselves with picks for next years draft, coming in with 2 high quality first (their own, and ATL), and with a third potentially right outside the lottery from Chicago. The pick back to MN is an interesting twist, I think MN would try for it, but it's definitely not a guarantee.
Starters: George, Sexton, J. Collins, Hendricks, Kessler Bench: Basically their 2024 draft class, Eubanks, Z. Collins