Experience with anti-mold additives?

Good morning everyone,

we are currently renovating the bathroom because we found two dark spots. The suspicion that there is mold under the wallpaper has not been confirmed. Apparently, it is only superficial on the wallpaper (which was painted extremely thickly in places).
Nevertheless, I wiped the plaster at the spots with Domestos. The ceiling is suspended with drywall panels.

About the surroundings:

One window, no roller blind. Shower and bathtub.
Tiles go up to the door edge, beyond that it is wallpapered.

Now my question to prevent such a case:
Is it worth buying an "anti-mold" paint additive and mixing it with the paint?
A few euros don't matter, and I would be comfortable if the wall is treated fungicidally but not sealed.

What can be used there? Alpina-Weiß? Paint from the painter's supply? Additive from Mellerud?
According to laser temperature measurement there are no thermal bridges at the spots (at least nothing punctual).

I would really appreciate answers and thank you in advance.

Best regards,
Daniel

There are FA-preconfigured interior paints available in specialist shops.