Since we were asked a lot about this, we reached out to porting studio Feral Interactive to see if they had any plans to update their Linux ports for the Steam Deck.
Feral have ported a number of titles to Linux in the past including Alien Isolation, XCOM & XCOM 2, Total War: WARHAMMER I & II, Total War: THREE KINGDOMS, HITMAN, the Tomb Raider series, Life is Strange & Before the Storm & Life is Strange 2, Dirt Rally and the list goes on. They also have a port of Total War: WARHAMMER III upcoming in "Early Spring".
After waiting quite a while, they replied today with an official statement about Steam Deck support:
Our most recent Linux titles are officially supported on Ubuntu only, and we do not currently have any plans to update games for further compatibility with Steam Deck or its operating system, SteamOS 3.0. If players encounter issues with Feral's native Linux versions of games on Steam Deck, we recommend playing them via Proton.