ᐅ Insulating the interior side of a garage wall with XPS foam?

Unfortunately, several contacted contractors (site visits completed) have let me down for months regarding the necessary thermal insulation (no quotes received). Therefore, I now want to insulate a garage wall (attached garage to the house) inside the garage on my own. The wall in question separates the heated kitchen/bathroom from the unheated garage. Unfortunately, a concrete block with a very poor U-value was used during construction.

Is XPS suitable for wall insulation, or is EPS sufficient?

Reason: The garage is expected to have increased humidity. Due to a built-in slope in the garage, rainwater runs behind a door and drips onto the garage door. Sometimes, this moisture can also reach the insulation.

Can XPS simply be plastered, or do you have to use special XPS boards?

Is it generally enough to bond the boards to the plastered and painted wall with appropriate adhesive (the wall will be cleaned and checked for loose plaster) and maybe use a few anchors? Or when should the boards be fully fixed with anchors? An adhesive test so far has been quite successful (holds firmly).