Switch to parsing the new Flutter version file bin/cache/flutter.version.json instead of the legacy one version and remove workaround #5231
Description
See:
- Flutter "version" file in repo root is missing and being created then deleted by the tool on branches named master/main flutter/flutter#142521 (comment)
- DevTools Performance page fails to load + other issues on Flutter master when 'version' file is missing #5226
We should also remove the workaround in dc897c3 once this is done.