How to diagnose and fix an odd Linux (Debian 12) networking failure with Starlink?

I'm having an odd issue on a Linux laptop (Debian 12) where after it connects to a subset of networks. It works for a second and then it cannot resolve hosts or retrieve any data. The same laptop can and has been used on other networks and even on a tether without any issues. However, when using it on a Starlink or a router connected to StarLink, it has these problems. Other devices, (phones and other laptops) connected to the Starlink network(s) work fine. Initially I thought it was a Wi-Fi connection issue as with enough time (minutes), requests from a browser would load. However, trying to

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