I'm a Sens fan, so just throwing that out there as I'm sure I'm coming in with my biases, and completely understand any Leaf fan dismissing a rival fan opinion right now.
With that out of the way, I think Matthews resigns, but it will be at a price point significantly higher than what we've seen top players sign at.
There's been rumblings that agents want to see top salary levels rise in the NHL, most notably by a comment from Kypreos. It's Kypreos, so it deserves some skepticism. But, his sources has usually been the player agent community, so, it's an area where he could have insight. If that sentiment exists, Matthews is the next big player up for a contract.
If Matthews is looking to set the new standard, Toronto is probably the team that is most likely to pay him. Owned by two media conglomerates, any GM or team president that says they can't make the salary work would get fired. A board of directors would see it as a simple decision to take the biggest name they've had on the Leafs and give him what he wants. Especially since the discussion will be happening around the same time that an extension for Pascal Siakam is being discussed, and that's trending towards a Supermax extension that'll make Matthews demands seem quaint (note: as a Raptors fan, MLSE should absolutely give Siakam what he's due).
The different league economics and team competitive concerns will be moot at that point. MLSE will want to keep the guy who makes them a lot of money.
I think a contract at the 20% max will happen. I think the term may not be as long though, to allow for reups as the cap goes up, but, NHLers tend to value security, so hard to judge that.