Issue description: DevTools Network screen non-functional after app
hot restart.
What is the fix: Correct a race condition in re-instating vm service
extensions after a hot restart.
Why cherry-pick: Users have complained much about this issue.
Risk: low, this fix has been in the main channel for a while.
Issue link: flutter/devtools#9203

Cherry-pick: flutter/devtools@v2.45.1...2.45.2
Change-Id: Ia28ae28179473af22b255bda77eda9a6e749b15e
Reviewed-on: https://dart-review.googlesource.com/c/sdk/+/442004
Reviewed-by: Alexander Thomas <athom@google.com>
Reviewed-by: Elliott Brooks <elliottbrooks@google.com>
Commit-Queue: Samuel Rawlins <srawlins@google.com>

Issue description: When users click 'Clear' in the DevTools Network
screen, they can see many assertion errors in the app console.
What is the fix: The assertion is erroneous, and is removed.
Why cherry-pick: The errors and stack traces are very disturbing to users.
Risk: Low, this fix has landed on the main channel and is tested on the same infrastructure.
Issue link(s): #61187

Cherry-pick: https://dart-review.googlesource.com/c/sdk/+/442260
CoreLibraryReviewExempt:dart-io
Change-Id: I1f095bb46e903637c63b639ad8bd2469e5e5f3dc
Reviewed-on: https://dart-review.googlesource.com/c/sdk/+/442700
Reviewed-by: Ben Konyi <bkonyi@google.com>
Reviewed-by: Alexander Thomas <athom@google.com>

Change-Id: I28a68326facfe52af8d8edb915c3531929e34e57
Reviewed-on: https://dart-review.googlesource.com/c/sdk/+/442940
Commit-Queue: Samuel Rawlins <srawlins@google.com>
Reviewed-by: Alexander Thomas <athom@google.com>