This is a refactoring to simplify how flutter test runs tests with FlutterTestPlatform.

Currently, the tester can crash before and after the test harness connects to the websocket, with the use of InitialResult. The control flow is nested, resulting in the rough state diagram below:

       Start tester
            |
   Observatory connected
    /                \
Websocket connected   Tester Process Crash (1)
    |
Connect to websocket,
run test 
    |       \
All ok     Tester Process Crash (2)

Instead, in this PR, we share the same crash state, which simplifies the logic and makes the workflow easier to reason about.

       Start tester
            |
   Observatory connected
    /                \
Websocket connected---\
    |                  \
Connect to websocket,---\
run test                 \
    |                     \
All ok                 Tester Process Crash 
                      

Other more minor changes:

• Skip waiting for the observatory, and just wait for the remote webSocket connection because this is what is really needed
• Currently, we don't call Watcher?.handleTestCrashed when the tester crashes after the harness connects to it, but we do call it when the tester crashes before the harness connects to it. This is fixed here.
• We also don't call watcher?.handleStartedProcess(ProcessEvent(ourTestCount, process, processObservatoryUri)) when enableObservatory is false. The code path is only active when that is enabled, which is fixed here with the refactoring to use a helper method to deal with connecting to the observatory. Because of this, we need to fix the package:integration_test tests
• Remove when from _getExitCodeMessage for simplicity, so that we don't have to track the state of the test purely for logging purposes. This doesn't seem useful because when is mainly an implementation detail. When troubleshooting (in verbose mode), the trace messages added would be much more useful in determining the state of the test, and some additional trace messages have been added.
• Remove InitialResult, TestResult, introduce a private _TestHarnessStatus

Existing tests should cover this refactoring.

Related: #66264. This PR will make it easier to decouple FlutterPlatform from Process (#74236)