I'm going to plant my flag and claim that we get both.
We have talked about the cap issues for both this season and next, so I'm not going to dive into those too much, as I do believe they create a massive headache for the Oilers to resign Drai and Bouchard. One thing I do want to note - that Kane's NMC becomes a modified 16 team list - so if he wants to stay on the Oilers for all of next year he simply only approves trades to teams with zero cap space to take him. Everyone is kinda handwaving away the fact that the Oilers would be able to trade him once his NMC modifies, but I'm not really sure it's that simple, as he can basically take all the crappy non-playoff teams who could eat a cap dump off the table.
A less talked about side to this, and why I think they might not match either player - The Oilers could actually use some mid-round draft picks for the upcoming TDL. At the current moment, the highest pick Edmonton has this year is a 4th. If anyone gets hurt, or is under performing, etc, the Oilers have very limited capital to make a move - especially if they need to move Kane mid-season, which they almost certainly will if they match both. I'm sure moving Kane will cost an asset, as no one is going to take a 5+M contract for this year and next for free. They still have the full slate of 2026 picks, but most teams want picks for the upcoming draft, so this hurts the Oilers bargining power during the TDL when they are supposed to be all-in.
Anyway, I'm sure two minutes after I post this the Oilers will match both, since that literally happened the last time I made a prediction