Room cold at the feet - Is basement ceiling insulation useful?

how should one fill the resulting gaps?

Mineral wool or foam work well.

Foam is pretty cool, you just have to be careful when working with EPS. they don't like each other.

OK
Used 10cm aluminum-coated PUR boards.
What can I do to make them white, is something like wallpapering common?

What can I do to get them white, is wallpapering common for that?

You can paint (if the paint holds) or actually wallpaper. Alternatively, you do a little more work - stick on 9.5mm drywall, fill and then paint (that’s what I’m currently doing in an extension).

Then I would foam up gaps. That fits together. For basements, I find it exaggerated, but if you really want to, you can probably paint on it with acrylic paint. It actually sticks everywhere.

I would like to avoid another gluing step with Rigips, after all it's just the basement :) I will look into acrylic paint, if in doubt I'll wallpaper - practical if you like doing that anyway ;)