Originally posted by _I_:

you can play different games at the same time,

Not from the same library, you can't.

from Steams documentation:

Can two users share a library and both play at the same time?
No, a shared library may only be played by one user at a time including the owner and even if they want to play different games.

https://help.steampowered.com/en/faqs/view/57A7-503C-991F-E9A8#simultaneous