Aha, it was Steam plugin bug.
For some unknown reason it couldn't be updated (I have no idea why, it haven't any special attributes, can be edited manually, and I was able to remove it after all). If I do "check for updates", it always found new Steam.dll, but not installs it.
As it already installed, it not seen in "Plugin updater" settings.
Simultaneously, it was invisible in "plugins", and didn't work in general.
Fix: remove dll altogether and install it from updater afterwards.