fix(web): show command output in work log - #4083

💭 The diff only modifies session logic and tests, which don't involve UI or styling, so there shouldn't be any findings related to the component system or Tailwind consistency check. I need to format the response as JSON while keeping the message simple—setting the state to success and putting "All clear" in the title and summary fields to satisfy both the schema requirements and the instruction to return exactly that phrase when there are no findings.