Factory page in the T3 web app #28

Outcome

The T3 web app shows the factory's runs next to its threads.

Acceptance criteria

• apps/web/src/routes/factory.tsx lists runs with repo, issue, state, current step, age and pull request link, and has pause/resume claims.
• apps/web/src/routes/factory.$runId.tsx shows a run's ledger events, its last gate output, a link to its thread, and a stop button.
• One nav link reaches the page. Its file and apps/web/src/routeTree.gen.ts are listed in factory/SEAMS.
• Components live under apps/web/src/factory/ with component tests for the empty, loading, error and populated states.
• /factory lists the open attention items from Needs attention: keep a list of what needs a person and notify on the Mac #58 at the top, and its nav link shows their count as a badge (hidden at zero).

Depends on

• Factory HTTP API for status, runs and control #27
• Needs attention: keep a list of what needs a person and notify on the Mac #58

Notes

This issue is for the fork's own factory, after the handover in #21. Leave it at factory:proposed until the fork's factory watches this repo.

Reference

• softfac, the Rust factory this ports, pinned at rawphp/softfac@bf273a1. Read it from a separate clone: git clone --filter=blob:none https://github.com/rawphp/softfac /tmp/softfac-ref && git -C /tmp/softfac-ref checkout bf273a1d93651992b4fc95b4dd6c111f8f3322cf. Its docs/lifecycle.md, docs/reference/ledger.md and docs/issues.md describe the behaviour; its tests pin it.
• Design: factory/docs/design.md in this repo.
• Upstream's AGENTS.md applies. Run only the tests and typechecks for the paths you touch (vp test run <path>, vp run --filter t3 typecheck), never the repo-wide checks.
• Edit no upstream file that is not listed in factory/SEAMS. A new seam needs a line in factory/SEAMS and a reason in the PR body.
• Port behaviour, not code: port the named test cases first (TypeScript, vitest / @effect/vitest), then make them pass. Exact comment and ledger wording is ported as is.