[2022] How to add Steam version to Paradox Launcher?

You must have run the launcher from the desktop shortcut, which is a standalone mode for users who do not want to run Steam. It does need a separate game installation if used that way.

As you are okay with Steam , run the game from the PLAY button in your library there, as before.

Aleorn said: But now, when I have my game installed in Steam but not yet linked to PDX Launcher, the saves look like some cryptic stuff. What could be the reason for that?

They are compressed. To uncompress them change the filename to add .zip to the end then double click on them.  

You might check with the folks in User Mods then, they'll have more experience in that area.

Good luck!