Speed up integration testing on the CI (taking around ~21 right now 09/23)

[kenzieschmoll]

example run that took 47 min: https://github.com/flutter/devtools/actions/runs/5336567626/jobs/9671473410?pr=5919

We should see if there is anything we can do to shard these or share steps that we are already doing for other jobs (e.g. code generation). Perhaps we could run the test in 3-4 different shards and make each shard its own job that can run concurrently. We may also consider sharing the step to start chrome driver and shut it down, as right now this is happening for each test, not once for running all tests. This is not that expensive though looking at the timing logs, but it could be a small win.

[kenzieschmoll]

After the above two referenced PRs, the longest integration test job now takes 27 min.

[kenzieschmoll]

In this example run before sharding, the integration tests had the following runtimes:

• flutter: 33m 16s
• flutter-web: 23m, 27s
• dart-cli: 17m, 14s

After https://github.com/flutter/devtools/pull/6385, the run times for the flutter and flutter-web devices (where we've added sharding) are down significantly:

• flutter integration tests runtime reduced by 40% (~33min to ~19min)
• flutter-web integration tests runtime reduced by 24% (~23min to ~17min)

[kenzieschmoll]

We should continue to investigate how to drive this time down further by sharing more prep tasks across jobs (getting deps or generating mocks).