Kubuntu 20.04 not resolving .local names any more all of a sudden
Solution 1:
It turned out it was some kind of temporary hardware failure on my docking station. By the way, it's an i-tec USB 3.0 Docking Station, featuring a DisplayLink DL-3900 chipset.
Unplugging the docking station from the AC outlet and plugging it back in fixed the problem. This explains why a system restore with Timeshift did not solve the problem, confirming that nothing had changed on my system. It was probably due to a couple of blackouts that occurred during the last weeks, one of which probably temporarily screwed up something in the docking station running behaviour.
Nevertheless, it's a really strange problem, never happened so far during several years of use: apart from this problem with mDNS, networking was working fine, as well as all the docking station USB ports or even the USB-to-HDMI video feature.