merge(plane): ax task lifecycle -- resume, stay-up runner, delivery as completion

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01EmM1j46qgKMh3zqD1QMwEo

benchmarks/measurements/2026-09-08-module-audit.json

@@ -1,7 +1,7 @@
 {
-  "modules": 129,
+  "modules": 130,
   "counts": {
-    "load_bearing": 120,
+    "load_bearing": 121,
     "standalone_capability": 9
   },
   "orphaned": [],
@@ -674,6 +674,14 @@
         "plane.tasks.verify"
       ]
     },
+    {
+      "module": "plane.doctor",
+      "classification": "load_bearing",
+      "reason": "reachable from gate, map_gate, pair_gate or the CLI",
+      "importers": [
+        "plane.reconciler"
+      ]
+    },
     {
       "module": "plane.generate",
       "classification": "load_bearing",