feat(CUST-WP-0014): repo sync automation & Gitea inventory

- Migration e2f3a4b5c6d7: add last_state_synced_at to managed_repos
- consistency_check.py: PATCH last_state_synced_at after fix run;
  fix ~ treated as non-empty state_hub_task_id (C-03 vs C-11);
  fix _inject_task_id_into_block skipping injection when field exists
  with null value
- install_hooks.sh: idempotent post-commit hook installer for all
  registered repos (make install-hooks REPO= / install-hooks-all)
- gitea_inventory.py: compare coulomb Gitea org against state-hub
  registered repos — registered / unregistered / hub-only sections
- infra/README.md: document systemd user timer + crontab fallback
- systemd user timer: custodian-sync.{service,timer} runs
  fix-consistency-all every 15 min (enabled)
- dashboard/src/repo-sync.md: Repo Sync Health page — sync age table,
  unregistered Gitea repos, hub-only repos
- api/routers/repos.py: GET /repos/{slug}/dispatch endpoint returning
  active goal, pending tasks per workstream, human interventions
- mcp_server/server.py: get_repo_dispatch() MCP tool

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

mcp_server/server.py

@@ -1416,6 +1416,24 @@ def update_repo_goal(
     return json.dumps(goal, indent=2)
 
 
+@mcp.tool()
+def get_repo_dispatch(repo_slug: str) -> str:
+    """Return active workstreams, pending tasks, and goal for a repo.
+
+    Use this at the start of a repo agent session to discover what work is
+    pending without needing to read the full state summary or scan workplan
+    files. The response includes:
+      - active_goal: the highest-priority active repo goal
+      - active_workstreams: list of active workstreams with pending tasks
+      - human_interventions: tasks that need human input (needs_human=true)
+      - last_state_synced_at: when the repo was last synced to the hub
+
+    Args:
+        repo_slug: Slug of the repository (e.g. 'marki-docx')
+    """
+    return json.dumps(_get(f"/repos/{repo_slug}/dispatch"), indent=2)
+
+
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