Log every run on the public site

Every firstrun run inside this checkout now writes its replay to docs/runs and adds a row to docs/runs/index.json. firstrun publish --all rebuilds the log from the runs folder, and 48 runs are backfilled. The new /runs/ page lists them with search, result filters and each run's cost against the plan's per-run caps.

Also records the Altimate Code quickstart run as a replay example, fixes .gitignore so it no longer hides docs/runs, and keeps the test suite from writing into the site log.