I think this story is much larger than it seems.
*I* think Don has been trying to move JDB for several years now and just not gotten any offers that were not lowball ones. Better to keep an assest who has higher value to you than to let him go for less value in return. The problem is Jakes value to other teams has not really increased.
I could see Don keeping him as an own rental. However, given his response to such situations in the past he might just skate through his last few months here.
Dont know about you, but I would rather have a player here who wants to play and will do so reliably.
It wouldn't be in DeBrusk's interests just to glide out the season even if he knows he's no longer wanted and/or wants to go elsewhere. As you said, his value hasn't increased of late, so it's not like the hard yards have already been done and he can now just wait it out for a nice big pay day. It may well be that he already has something on the table, for example if the Oilers or whoever have assured him they want to sign him and pay him x amount but not 'til the offseason. In that case he could just drift along, but it seems unlikely.
That said, human nature is fickle, and if Jake knows his time in Boston is drawing to a close, one way or another, it may negatively affect his mindset and his play even if it's counterproductive. And in that sense I agree with you - if Jake really wants to stay and the Bruins do too then get a deal done, otherwise if either party is lukewarm then get busy and find what value you can by bringing in someone/s who really wants to commit to Boston. Act one way or the other, prevaricating helps nobody.
My impression has always been that DeBrusk likes being a Bruin, and he's committed to it and the team in his own way, but it's not heart and soul for him. I can easily imagine him in another jersey. He's different than, say, Gryz, who for various pretty obvious reasons really seems desperate to stay in Boston. For better or worse, and speculation aside, my gut says he's out the door. In which case it's on the GM to not screw up how that happens and to optimize the parting. However I was also fairly convinced that Jake was gone in 2021, yet here we are. It could well be that even at this late hour the outcome is not set in stone.