DWDS may not reuse the underlying connection upon refresh

We [check](https://github.com/dart-lang/webdev/blob/83f661c80b902e8bd7186e9739a7bcb9c22bef8e/dwds/lib/src/handlers/dev_handler.dart#L373) if the `existingConnection` `isInAKeepAlive` state so that we can reuse the connection. Until recently, a refresh would trigger the [done](https://github.com/dart-lang/sse/blob/8add37c0ec0419ce28153a03f299d44ce006a975/lib/src/server/sse_handler.dart#L238) event within `package:sse` prior to us trying to create an isolate. Now, there appears to be delay with this event. Thus the `canReuseConnection` check fails. I'm not sure if this is a regression in Chrome or some other part of infrastructure.

Start with the canReuseConnection check and existingConnection handling in dwds/lib/src/handlers/dev_handler.dart around line 373, then compare the done event in package:sse at lib/src/server/sse_handler.dart around line 238. Trace refresh event ordering and confirm that an eligible underlying connection is reused after refresh without the check failing.

Written by the indexing model from the issue text.