OK now I got it working.
1st I rebooted the mac hosting my library (not sure if this made any difference tbh), then tried again.
The behaviour on the iOS18 device was the same as before, with no visible reaction after selecting the home sharing library. However after approx. 3 - 4 minutes of seemingly doing nothing, the display suddenly switched to show the home sharing library.
I do have quite a large media library on my mac, and it does take a minute or two for my iOS17 devices to load it as well. But at least in iOS17 there is an indication that the connection was in progress. In iOS18 however there seems to be no visual indication that it is doing anything during the connection process.