fix(input): durable exactly-once input delivery so a dropped link can't lose a prompt

A "sent" prompt could vanish with no trace on a flaky connection (e.g. a train):
with local echo on, Enter cleared the overlay then sent over the WebSocket
fire-and-forget. On a half-open socket (readyState===OPEN, dead TCP) ws.send()
doesn't throw, so the frame was silently discarded, nothing was enqueued, and
navigator.onLine stayed true — the prompt was lost and never resent.

Replace the best-effort offline queue with a durable, acknowledged delivery layer:

- Client (app.js): every input frame is recorded with a stable clientId +
  monotonic per-session seq and persisted to localStorage BEFORE delivery, and
  only dropped on a server ACK. Delivered over WS (acked via {t:'ia',seq}) or,
  when the socket is down, POST in seq order (HTTP 2xx = ACK). A 2s sweep
  force-reconnects a WS whose oldest frame is unacked past 4s (half-open sockets
  never recover on their own); on reconnect/reload all pending frames re-deliver.
  Survives reconnects AND page reloads. Connection indicator shows pending count.
- Server: Session.shouldApplyInput(clientId, seq) applies each frame exactly once
  (bounded MRU map); ws-routes + POST /input dedup a redelivered seq but still ACK
  it (200 / {t:'ia'}), so an at-least-once resend can never type the prompt twice.
  Untagged input (curl/legacy) applies unconditionally — no behavior change.
- terminal-ui.js sendInput() (voice / keyboard-accessory / paste) now routes
  through the same durable layer.

Tests: test/reliable-input-dedup.test.ts (exactly-once semantics on the real
Session) + POST /input dedup route tests. Design: docs/reliable-input-delivery.md.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

src/web/public/terminal-ui.js

@@ -2195,12 +2195,11 @@ Object.assign(CodemanApp.prototype, {
    * @returns {Promise<void>}
    */
   async sendInput(input) {
-    if (!this.activeSessionId) return;
-    await fetch(`/api/sessions/${this.activeSessionId}/input`, {
-      method: 'POST',
-      headers: { 'Content-Type': 'application/json' },
-      body: JSON.stringify({ input, useMux: true }),
-    });
+    if (!this.activeSessionId || !input) return;
+    // Route through the durable, exactly-once delivery layer (useMux for the
+    // POST fallback) so voice / keyboard-accessory / paste input also survives a
+    // dropped link instead of being lost in a single best-effort fetch.
+    this._sendInputAsync(this.activeSessionId, input, { useMux: true });
   },
 
   // ═══════════════════════════════════════════════════════════════