OK...so EDIT:
I reinstalled the game after it being uninstalled for...four years or so I believe.
Then I disabled the cloud
Then I deleted both required folders in Steamapps and in userdata (that were probably empty, as they appeared only after I installed the game and were not present before...or maybe they contained cloud saves). After that I checked the file integrity, which went without a hitch.

The game said there is no profile present so I created one.
I started new game and got a first cutscene (portal travel) without anything skipping, and saved the game (all empty files) right in the middle of first Remy conversation.

I see no gallery, no ingame achievments (tough Steam achievments are still present) and no status except "Remy - neutral" and I know I dated him years back and had a bad ending with him (and both bad and good ending with Adine)
I quit the game and tried to reactivate cloud again and the steam page noted that there is conflict in cloud and if I want to resolve it, so I deactivated it again, booted up the game just in case and everything is still empty except that mentioned new save.

This all leads me to believe that my safefiles are really clean state as I intended and I hope it will help others who may want to do this too.

I will confirm this once I tried to play the game a bit and find out IF it really is wiped clean

Gallery is dependent on getting good endings with characters or completing side character meetings (which is only possible after completing an ending.)

Best way to check you have a clean slate is to look for any character sprites or their shadows on the main menu. But if you deleted the folders you indicated you did, that should take the persistence files with it, and therefore clean your slate.

You should be good.

There are 3 types of save files:
-the classic ones, those who have numbers and represent the majority of your saves
-persistent, which is a persistent save
-awsw, another persistent save, that is not in the same save folder. It is somewhere where programs save user-specific data (userdata maybe)

Also, I saw that the save folder appeared both in the steam folder, and in the user-specific folder (userdata I think). As the previous comment said, you should be good.