Another new stable Steam-Client 07.10.2021 has been released for Linux. It contains an improved Vulkan-Shader-caching among other things:
Steam Client Update, October 7
A new Steam client has been released and will be automatically downloaded.
When Steam detects a game file has been corrupted, it will now try to reuse as much of the corrupted file as possible to save bandwidth when downloading correct data for that file
Fix bug causing slow reconnect to Steam after resuming from a system suspend