Unless Alek's behaviour is really THAT bad, there is no way the Jays are shopping him. He will likely bounce back, and, if he goes, now the Jays have a big hole in their rotation that Tiedman isn't ready to fill, and in two years, the starting rotation is now just Berrios and likely Tiedman. With Manoah, you still got something, and if Bassitt pulls an Estrada, which is very possible he will do, he will be more likely to stick around if he sees three good pitchers still with the team. Now that's a good looking 4 man rotation.
If the Jays are actually considering trading Bichette, which I doubt, it's because Bichette has made it be known he has no intention of resigning with the Jays AND someone has offered them a rather nice package. Consider how many interesting shortstop prospects they have right now, it could be worthwhile to give them a chance to mature into proper MLB players rather than leaving them down on the farm. This is especially true if they manage to nab a good 3B. Combined with Martinez and potential offense from Schneider, which I doubt he'll be able to replicate, plus whatever huge package they could get, I imagine the Jays would consider it a fair outcome for a player that will walk in a couple years and would fetch much less with just one year on his contract. And given the Jays competitive window ends in two years when the starting pitching will just be Manoah, Tiedman, and Berrios, it could be a good idea to load up on big time prospects now rather than later.
But again, I doubt they give up their most consistent hitter when offense was their biggest problem this season. And they could just trade him next year if they must.