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/routes/session-routes.ts

@@ -662,7 +662,7 @@ export function registerSessionRoutes(
 
   app.post('/api/sessions/:id/input', async (req) => {
     const { id } = req.params as { id: string };
-    const { input, useMux } = parseBody(SessionInputWithLimitSchema, req.body);
+    const { input, useMux, seq, clientId } = parseBody(SessionInputWithLimitSchema, req.body);
     const session = findSessionOrFail(ctx, id);
 
     const inputStr = String(input);
@@ -673,6 +673,13 @@ export function registerSessionRoutes(
       );
     }
 
+    // Reliable delivery (POST fallback when the WebSocket is down): a 2xx IS the
+    // client's ACK, so a tagged duplicate redelivery must still return 200 but
+    // skip the write. Untagged requests (curl/legacy) always apply.
+    if (typeof clientId === 'string' && typeof seq === 'number' && !session.shouldApplyInput(clientId, seq)) {
+      return {};
+    }
+
     // Write input to PTY. Direct write is synchronous; writeViaMux
     // (tmux send-keys) is fire-and-forget to avoid blocking the HTTP response.
     if (useMux) {