Finally I solved the issue with instable wifi, which was disconnecting and reconnecting several times per hour.
It looks like the FP3(+) is a bit picky with access points. Since I removed my older TP-Link access point and using a FritzBox 7590 instead, the reconnects are gone. There is now stable wifi on my FP3+.
And 5 GHz is working again too, after doing the workaround mentioned there.