We've created a special Linux port of Murderous Muses including webm (not mp4) videos so that everything plays as smoothly as possible. Cloud saves work between PC, Mac and Steam Deck.
The touchscreen has been disabled so we've included a pop-up keyboard for seed entry (the only place in the game it's needed) but other than that it's the same codebase as PC and shares all the same features.
We're not currently planning on adding any additional features for Steam Deck compatibilty until Valve take a look at it for their official list, but let us know in discussions or by emailing support if there's any must-have feature you'd like to see.
We hope you enjoy playing Murderous Muses on Steam Deck!