* Move web integration tool tests to web.shard
Web integration tool tests depend on DDC changes in SDK. This change
moves them to a separate shard and subshard so CI bot configurations
can run them separately.
In particular, with will allow running those tests on dart CI flutter
HHH web bot instead of a non-web one, allowing early detection and easy
classification of issues caused by SDK changes as VM- or Web related.
* Enabled verbose mode for flaky web_tool_tests
* Split out the test changes to be commited first
