Official Linux support is not confirmed. BULKHEAD’s September 4 update said Proton support was still in development; the current Steam listing specifies Windows.
The official support position
The developer’s Linux update says support was not official and could not be promised for the Early Access launch. As of September 13, official Linux support remains unconfirmed.
Steam lists Windows requirements and Elytra anti-cheat. Linux compatibility may change as development continues.
What about Steam Deck?
As of September 13, SteamDB lists Steam Deck / SteamOS as Unsupported, based on a September 11 compatibility test for build 25254499.
A broad Linux tag elsewhere on a data page is not equivalent to a verified multiplayer session. Check the current official compatibility information before depending on a Deck installation.
Why old beta videos are not enough
An August video or a successful launch into a training area may refer to a different build and anti-cheat state. It does not demonstrate that the released version can join and sustain a multiplayer match.
A useful compatibility report needs the distribution, Proton version, GPU and driver, game build, and whether actual online play succeeded.