Thanks for your great advice! I did a quick measurement of the noise spectrum inside the cabinet with my phone:

It seems most of the noise is in the 100 - 1k Hz range.

Basotect looks perfect! It is also quite affordable. Will 3 cm will suffice or would you recommend thicker padding?

(If I can't find a proper solution for the cable ducts, I could use any remaining Basotect, glue it together and fill the duct with it. There will be just a few cables that have to leave the cabinet anyway…)

Of course, I will do a follow up afterwards :)