docs(remote): correct what the wake PR moved

- `host-wake-ui.js` joins the documented load order (12.2) and gets its
  `@dependency`/`@loadorder` tags; the frontend module count is 33, not 32.
- `remote-wake` is not "(pure)" — the module uses `dgram`/`net`/`child_process`.
- SSE counts: 160 constants, and the category is "Remote auto-reconnect / wake
  (5)"; the route table's per-file counts are refreshed (sessions 37, cases 34).
- The CLAUDE.md wake rule now names the create/attach wake, the 40 s request
  budget, the whole-chunk paste drop, the registry's lifetime (drop on cleanup,
  stop on shutdown) and the deliberately non-wake-aware WebSocket keystroke
  path — that paragraph is what the next person reads.
- Reverted the eight lines of unrelated Prettier markdown churn in
  `docs/architecture-invariants.md` (docs/ is not in the format glob, so it was
  an editor): only the new wake paragraph remains in the diff.

src/web/sse-events.ts

@@ -5,7 +5,7 @@
  * and referenced by the frontend (`SSE_EVENTS` in `constants.js`).
  * Both files MUST be kept in sync.
  *
- * 158 event constants organized by category:
+ * 160 event constants organized by category:
  * - **Core** (1): init
  * - **Transport** (1): sse:heartbeat
  * - **Session lifecycle** (23): created, updated, deleted, terminal, idle, working, ...
@@ -14,7 +14,7 @@
  * - **Session: Plan** (4): planTaskUpdate, planCheckpoint, planRollback, planTaskAdded
  * - **Tasks** (4): created, completed, failed, updated
  * - **Mux** (4): created, killed, died, statsUpdated
- * - **Remote auto-reconnect** (3): sessionDropped, sessionReconnected, reconnectExhausted
+ * - **Remote auto-reconnect / wake** (5): sessionDropped, sessionReconnected, reconnectExhausted, hostWaking, hostWakeFailed
  * - **Respawn** (24): stateChanged, cycleStarted/Completed, step*, aiCheck*, planCheck*, timer*, log, ...
  * - **Subagents** (7): discovered, updated, tool_call, tool_result, progress, message, completed
  * - **Workflow runs** (3): run_discovered, run_updated, run_removed (ultracode / Workflow tool)
@@ -176,7 +176,7 @@ export const MuxDied = 'mux:died' as const;
 /** tmux session stats refreshed. */
 export const MuxStatsUpdated = 'mux:statsUpdated' as const;
 
-// ─── Remote auto-reconnect (COD-108) ─────────────────────────────────────────
+// ─── Remote auto-reconnect (COD-108) + wake-on-LAN ───────────────────────────
 
 /** A remote session's local ssh pane died; an auto-reconnect attempt is starting. */
 export const RemoteSessionDropped = 'remote:sessionDropped' as const;