Definitely not an Android thing. I, and various friends and family, have been using Google Messages for Web for years (as well as MS Phone Link), across a wide range of devices and connections and have never had those issues. Sometimes I stay connected for days at a time on Google. I suspect this is going to keep happening regardless of what service you use until you figure out what the underlying issue is with your phone/service/internet etc. I would think that if this is happening with a wired, MS Phone Link connection, the culprit is most likely your service provider.
I thought the same thing, but the fact that those ruins seemed familiar makes me wonder if maybe there's more to it than that.