Based on today’s gaming sessions I think my dressing room error is pretty much solved.
I finally went and bought a separate WLAN router since I haven’t been happy with my cable modem WLAN anyway. I configured my modem to bridged mode and connected my new WLAN router to that. Then I connected the PS4 to the WLAN router with a cable.
Now it seems idle connection are not dropped anymore because I was able to play multiple CHEL games including EASHL and Ones.
Obviously this doesn’t mean you all should go and spend money on new devices, but for me it might have solved the issue (still not 100% sure, more testing needed) as a bonus when I actually wanted to improve my WI-FI range and reliability.
Hopefully there’s a patch from EA coming soon to fix it for everyone...