It seems games not showing as installed after installation is common enough that steam made this page -
https://support.steampowered.com/kb_article.php?ref=8379-RYIP-2998
I assume when shut PC down at night you just use the power button in the start menu? I seen someone hit reset at shutdown and it broke windows. shutdown can affect restart next day on systems with fast start up on (I know I suggested you turn it off already)
try running chkdsk on the ssd
boot in command prompt (admin), type
chkdsk c: /f
if you install games in the hdd, run chkdsk x: /f /r on it as well (replace x with drive letter of hdd)
and press enter. 2 paragraphs will pop up, agree to run on startup and restart PC
right click start button
choose powershell (admin)
type
SFC /scannow and press enter
once its completed, copy/paste this command into same window:
Repair-WindowsImage -Online -RestoreHealth
and press enter
SFC fixes system files, second command cleans image files, re run SFC if it failed to fix all files and restart PC