A run log's lines on /runs draw §5's row and a badge for their kind, on the server and live #4603

Done:

• [ ] src/web/pages/runs.ts and src/web/studio/log.ts draw each log line as §5's row with a badge naming its kind (you, say, tool, forge, pulse)
• [ ] src/web/client.ts appends live lines with the same markup
• [ ] no ln- class is in the markup; a test fetches a run page and asserts it

Run bun scripts/design-lint.ts and bun test test/design-lint.test.ts before pushing; where counts fall, lower docs/design/baseline.json in the same pull. Replaces #4226: the crew's two tries went red on tests this change does not touch (those are planned separately), so keep the diff to the files named.