DevTools is cached across Flutter version changes

Steps to reproduce:

1. Make sure Flutter version matches Flutter main channel
2. Run a Flutter app
3. Open up DevTools, check DevTools version
4. Close DevTools window
5. Switch Flutter channels (e.g. to stable channel)
6. Run a Flutter app
7. Open up DevTools, check DevTools version

Expected: DevTools version should match the version on stable channel
Actual: DevTools version matches version on main channel

Note: If you then open up DevTools in an incognito window, the DevTools version is expected.

@ditman - I know you mention that the Flutter service worker will be removed. Do you know what the status of that is / could this be related? Thank you!