Pine Studio have confirmed their plan to launch Escape Simulator 2 in October, with a note about Steam Deck / Linux support. In case you missed it — they just recently dropped their Native Linux build for the first game.
With the release now confirmed for October 21st, they're giving out more info in an FAQ post that notes:
Q: What about Linux and Mac support?
A: A Mac version is planned. For Linux users, we'll ensure compatibility through Proton, optimizing for Steam Deck support from day one.
It's a shame to see no Native Linux support going forward, but if they do actually focus on making it will well with Proton, at least you'll still be able to click play on Linux systems like SteamOS / Steam Deck. We do find often that Proton gives a better experience than Native Linux builds, as some game engines are not particularly great on Linux.

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Other details from the FAQ post note they will add VR support, Escape Simulator 1 is still going to get updated, it has a darker atmosphere but nothing scary as it's still a puzzle game, up to 8 players can escape together and more.