refactor(ai): move reasoning helpers and the Coach error resolver into their own files

The reasoning separation grew three files past their size ratchet. The Local
client's reasoning collector and the new separation helpers move to
local-reasoning.ts, the gateway client's thinking room and reply separation
become two private methods, and the Coach's error-code resolver moves out of
chat-bubble.tsx into coach-error-key.ts, still re-exported from
message-thread.tsx. Code motion apart from comments that said when a branch
was added rather than what it does. The baselines record the shorter files.

Refs #1276

src/__tests__/baselines/source-function-lines.json

@@ -1,7 +1,7 @@
 {
   "$comment": "Production functions over 200 lines, keyed \"file :: name\", and their length. Maintained by src/__tests__/source-size-ratchet.test.ts.",
   "count": 352,
-  "total": 113984,
+  "total": 113949,
   "entries": {
     "app/achievements/page.tsx :: AchievementsPage": 206,
     "app/api/admin/backups/upload/route.ts :: apiHandler(arg)": 314,
@@ -251,12 +251,12 @@
     "lib/ai/coach/glp1-snapshot.ts :: buildGlp1SnapshotBlock": 218,
     "lib/ai/coach/snapshot.ts :: buildCoachSnapshotImpl": 882,
     "lib/ai/coach/tools/loop.ts :: runCoachToolLoop": 438,
-    "lib/ai/coach/turn/model.ts :: runTurnModel": 560,
+    "lib/ai/coach/turn/model.ts :: runTurnModel": 540,
     "lib/ai/coach/turn/pipeline.ts :: runTurn": 274,
     "lib/ai/coach/turn/reply-guards.ts :: guardReply": 331,
     "lib/ai/codex-client.ts :: parseResponse": 302,
     "lib/ai/local-client.ts :: generateCompletionStream": 298,
-    "lib/ai/openai-client.ts :: generateCompletion": 390,
+    "lib/ai/openai-client.ts :: generateCompletion": 375,
     "lib/analytics/bp-in-target-fast-path.ts :: computeFromRollups": 203,
     "lib/analytics/compliance/display.ts :: calculateCompliance": 212,
     "lib/analytics/correlations-fast-path.ts :: computeCorrelationHypothesesFastPath": 256,