Debug stepping/pausing with Dart Debug extensions is very slow with remote servers

When running on GitPod, it takes around 10 seconds for a breakpoint to be hit. I previously assumed this was [the Chrome issue](https://github.com/dart-lang/sdk/issues/39187) but if I open the inspector for the extension, I see around 138 (sequential) requests when a breakpoint was hit, ranging from 25ms to over 2s adding up to around 10s.

We're forcing WebSockets for the VM Service proxy from VS Code, but I don't think they're currently supported for the debug extension backend - I wonder if that would make a significant difference here?

Start by reproducing the breakpoint delay on GitPod or another remote server and inspect the Dart debug extension backend through its inspector. Trace the VM Service proxy path used by VS Code, including the forced-WebSocket configuration, and compare the sequential requests during stepping or pausing. Done means the cause is established and remote debugging no longer incurs the reported excessive delay.

Written by the indexing model from the issue text.