Investigate whether we can eliminate the SSE logic from DevTools app and DevTools server

The SSE connection logic (https://github.com/flutter/devtools/blob/master/packages/devtools_shared/lib/src/service/service.dart/#L97) is only ever hit when debugging a Web app in g3. If this is truly a g3-only need, then we should try to remove the dependency on this logic in our external source code and move it to a g3-only location.

This will reduce the number of dependencies we have to take on in the DevTools packages.

There are some SSE endpoint on the DevTools server in DDS that are confusing because they are not hit 99% of the time (non google3 connections). This needs to be investigated further to see if we can really remove the SSE logic from DevTools.

Start by reading the SSE connection logic in packages/devtools_shared/lib/src/service/service.dart around line 97, then trace the related SSE endpoints in the DevTools server in DDS. Determine whether the logic is used only for g3 Web debugging; done means documenting that finding and, if confirmed, identifying the external dependency and the g3-only location where it can be removed or moved.

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