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.

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.