Internet connection issue with Monterey

There's been some discussion of internet problems with Monterey 12.4.1. From what I've read, users have been in the middle of using some online resource and then get cut out. My issue is different. It's the initial access to the internet that is a problem. My network connection in preferences shows me connected and with an IP address, but in both Safari and Firefox it takes multiple attempts and various switching on and off, rebooting, etc. before I can connect. This issue affects both a 2021 iMac (with Apple M1) and an older MacBook from 2017. But (and this is the important point, I think) it does not affect another iMac in the same household running Big Sur. To make this more interesting, the MacBook connects flawlessly and quickly to the WiFi network at my job. So it looks like a specific interface problem between 12.4.1 and the ISP in my home, but not a problem between Big Sur and the very same ISP.