Harden iOS sign-in against stale-connection POST failures

iPad users hit a spurious "network error" on the first tap of
"Send sign-in link", with a second tap succeeding. Cause is iOS
Safari dispatching the POST onto a pooled keep-alive socket the
server/proxy already closed; unlike a GET it isn't transparently
re-sent, so it surfaces as a transport TypeError. The single 500ms
auto-retry was too quick and reused the same dead socket.

Both sign-in entry points (auth.html postWithRetry, index.html
fetchWithRetry) now retry 3x with growing backoff (0 -> +400ms ->
+1.6s) to outlast Safari evicting the socket. Frontend-only.

Ships as 0.2.156.

public/auth.html

@@ -335,22 +335,30 @@
         return;
       }
 
-      // Silent retry on the first fetch — iOS Safari sometimes
-      // aborts the very first request from a cold tab with a generic
-      // "Load failed" TypeError. A single ~500ms retry hides the
-      // flake; server-side errors (4xx/5xx) are not retried because
-      // they're deliberate responses, not transport issues.
+      // Silent retry on transport failures — iOS Safari can dispatch a
+      // POST onto a pooled keep-alive socket the server (or a proxy in
+      // front of it) has already closed. Unlike a GET, a non-idempotent
+      // POST isn't transparently re-sent on a fresh connection; it
+      // surfaces a "Load failed" TypeError instead. A single quick retry
+      // tends to reuse the same dead socket and fail again (the reported
+      // "first tap errors, second works"), so retry a few times with
+      // growing backoff to outlast Safari evicting the socket. Server
+      // errors (4xx/5xx) are returned as-is and never retried — they're
+      // deliberate responses, not transport flakes.
       const reqInit = {
         method: 'POST',
         headers: { 'Content-Type': 'application/json' },
         body: JSON.stringify({ email }),
       };
       async function postWithRetry() {
-        try {
-          return await fetch('/auth/request-link', reqInit);
-        } catch (e) {
-          await new Promise((r) => setTimeout(r, 500));
-          return await fetch('/auth/request-link', reqInit);
+        const backoffsMs = [400, 1200];
+        for (let attempt = 0; ; attempt++) {
+          try {
+            return await fetch('/auth/request-link', reqInit);
+          } catch (e) {
+            if (attempt >= backoffsMs.length) throw e;
+            await new Promise((r) => setTimeout(r, backoffsMs[attempt]));
+          }
         }
       }
       try {