Verify severe and shout log messages in tests.

[isoos]

• Tests runs should check whether any severe or shout-level log messages were emitted. #8422
• Builds on Remove tasks from post-test verifications. #8424 to reduce the noise it needs to verify for. Though apparently we also have a somewhat randomly appearing race issues with task-worker cleanup and also with local search availability in tests. These will should be addressed in follow-up PRs.
• When a test specifies expected messages, we also throw if the pattern is absent.
• I haven't investigated why the exported API test has unhandled errors yet, but these are the log messages we must specifically look into.