Implement Branch Gardener scheduled branch-hygiene skill

[BunsDev]

Scheduled branch hygiene as a familiar skill, per ROADMAP M2 and docs/branch-gardener.md.

• Classify branches (active, stale, dead, PRless).
• Delete dead branches under policy.
• Open draft PRs for PRless work that has commits.
• Report results to Cave.

Trust framing: visible action log, conservative defaults, Cave oversight before destructive ops.

See: docs/branch-gardener.md, ROADMAP.md (M2).

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Wave 1 grooming

This issue was the thinnest spec in the wave; grooming below brings it to the same execution-readiness bar as its peers.

• Size: M · Intra-wave rank: standalone lane — no code deps beyond Add durable task queue and GitHub delivery idempotency #2; no downstream blockers.
• Depends on: Add durable task queue and GitHub delivery idempotency #2 (queue/task state for scheduled runs). Unblocks: none.
• In scope: branch classifier (active/stale/dead/PRless); policy-gated dead-branch deletion; draft-PR open for PRless work with commits; Cave-visible action log + per-run report; conservative defaults; Cave oversight before destructive ops.
• Out of scope: general scheduling infra beyond the M2 queue; auto-merge; non-branch hygiene.
• Ready checklist:
  1. Branch classification from GitHub refs: last-commit age, PR association, ahead/behind.
  2. Policy: age thresholds, protected-branch exclusions, dry-run default, destructive-op gate requiring Cave approval.
  3. Actions: delete dead branch (policy + approval), open draft PR for PRless commits.
  4. Emit a structured action log + Cave report per run.
  5. Wire as a scheduled familiar skill triggered off the M2 queue.
  6. Tests: classifier fixtures; dry-run makes no writes; destructive op blocked without approval.
• Done when: classifier covers active/stale/dead/PRless; destructive ops gated + logged; dry-run default proven no-write; cargo check/clippy/test green. Refs: docs/branch-gardener.md, ROADMAP M2.