I'd be surprised if Elias and the O's are willing to outbid every other team for Burnes. Both due to how much weight they put into advanced stats and because they'll be competing with some very deep pocketed teams that just lost out on Soto.
I also have a theory that McCann and Burnes go to the same team. Burnes used him as his personal catcher last year and the O's signed Gary Sanchez to backup Adley.
And they're reporedly not one of the most aggressive teams for Crochet. They don't have the prospect capital that they used to. The Red Sox are reportedly after him too, and they may have the best farm system in the league now.
But
@eojsmada is right, the O's front office is pretty tight lipped.
My best guess is that they trade for another Eflin-type guy, a solid #2 type guy, or a #3 who can "play up" in the rotation as needed.