Steam doesn't do updates asap anymore.

Update downloads get scheduled for off-peak hours, sometimes leaving games un-updated for days. That means sometimes you go to play something, and it isn't up to date.

This isn't linux specific, it's like this for everyone. It prioritises keeping games you play a lot updated, and lags behind more on games you almost never play but just have installed.

There is no way to circumvent this. Steam wants to spread out when people download updates, so there isn't a giant spike in download server load whenever updates drop.

Updates only go out immediately to people actually playing the games, and then trickle out over time to the rest.

Also the constant "updates" that happen aren't game files. Steam is keeping up with the files it needs to keep shaders compiled for your games in advance (which has to be re-done every gpu driver/game update). If you don't want that, you can disable precompiling in steam settings.

Steam re-downloading these files constantly is a known issue, but to be clear, your game files are fine. Their updates work no differently from windows.

Mine updates everything automatically, and like the Windows version it sometimes schedules updates for a later date.

The only difference I notice between Linux and Windows versions is the shader cache updates.

this doesn't match my experience at all.