I've continued to puzzle over it.
If the laptop is on and connected by cable to the router, then all works correctly. If the laptop isn't on, or is connected by WiFI, then I get the error message.
The various devices all have fixed IPs on the router, but that's been the case forever, and the old laptop was the same.
The iThings don't appear at all in the (Windows) display and have never done so, but that doesn't surprise me.
This is the error message as it appears:
I don't think there's any problem with the router allowing the devices to see each other - the laptop and the desktop appear in each other's Explorer displays, and I can copy and move files to and from either with no problems.