PSA: Did not check before I bought, Steam Deck says unsupported. Huge bummer for me.
However, I found out through ProtonDB that it's an easy fix. Here's how I bumbled through it if, like me, you haven't done this before.
Open Desktop Mode, then in the Discover app, download ProtonUp-Qt. This lets you download and install versions of Proton GE easily. These are community extensions of normal Proton compatibility tool Steam uses, made by some kind of Linux warlocks.
Launch ProtonUp, click Add version.
Compatibility tool: Proton-GE
Version: GE-Proton10-17 (A newer version might work too, but I just installed exactly what ProtonDB said).
Install, close, boot back to game mode if you want.
Go to DMC Collection's properties, compatibility tab, "Force the use of a specific Steam Play compatibility tool". The GE proton you installed should be at the bottom of the list. Select it, close properties.
I played 20 minutes or so of the first one and it was fine (aside from the clunky old controls).