I'm close to 100% that they offer Jaylen something either at or just below the full designated player max, and that he takes it which means he's not getting traded.
If for some reason he rejected that, well the return is likely to be underwhelming, you're looking for 80 cents usually in those situations. Bridges+ from BKN would be my preference in player type and value. I actually looked back at the Utah possibility and feel better there than initially, I think I kind of lost track of Markkanen when he went to CLE, because the trendline on his defense surprised me... not good certainly but not as bad as it was.
This is where I'm at as well.
If Jaylen wants the supermax to stay, he stays.
If he rejects it, I think it would be him saying he wants out. As you said, it's tough to get full value in those situations since he would have to sacrifice even more money to extend with a new team. They'd have to wait for the season to play out and hope he does re-sign the following summer, which is really risky.
Mikal Bridges would also be my top target in that situation, I'd be looking for Bridges + DFS. An option I keep thinking about would be a three way deal with the main pieces being Bridges + DFS to Boston, Jaylen ending up with his favorite coach in the whole wide world in Houston, and the 4th pick ending up in Brooklyn. With Ime there, and in a pretty popular city for players, I think that might rank fairly highly on places Jaylen would re-sign. Maybe kill two birds with one stone for them and they can tell Harden, sorry no cap room for you.
Would depend on if Brooklyn thinks they can be a title contender with either Bridges or Jaylen as their lead guy, I can't imagine they do, and Houston/Ime deciding they can make a big step forward adding Jaylen to their young core rather than adding another teenager.