Integrate active metrics into request logs page

[BenItBuhner]

Summary

• Update the existing /logs page to show running requests with elapsed duration, estimated input tokens, output speed, and active status.
• Preserve the existing selected-request event timeline while adding active-aware metrics and table columns.

Validation

• bun run typecheck
• bun test tests/admin-events.test.ts
• cd web && bun run typecheck

Notes

• The backend active-log changes from this branch were already merged via PR Show in-flight requests in analytics logs #11; this PR carries the remaining logs-page integration commit.