Wire up the SSE push channel in both frontend dashboards

app/static/index.html: opens an EventSource against /rounds/stream (no auth
needed, see the previous commit) alongside the existing polling loops. On an
"update" notification, immediately re-runs the same refreshes polling would
eventually do (refreshRound/refreshMe/checkLastRoundResult when logged in,
refreshChainStatusOnly when logged out). Also reacts to the browser's "open"
event, which fires on the initial connection and on every automatic
reconnect — this re-syncs right away instead of leaving the page on stale
state until the next event or poll tick, which matters most right after a
dropped connection comes back.

app/static/admin.html: same channel, refreshing the chain-status bar and
whichever admin section is currently open (Utenti/Round/Transazioni
pendenti/Audit log) instead of requiring a manual tab switch to see new data.

Polling intervals are untouched in both pages — this is purely additive, so
a blocked/dropped SSE connection just degrades to the pre-existing behavior.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

app/static/index.html

@@ -682,8 +682,14 @@ async function showDashboard() {
   // data.winner_user_id === myUserId — otherwise that comparison could race
   // against an unset myUserId right after a reload.
   await refreshMe();
+  // Awaited too, and before refreshRound(): on a brand-new browser/device that
+  // never saw this round live (nothing in localStorage), this is the only
+  // thing that knows the outcome once the round has fully closed. Resolving
+  // it first means refreshRound() finds the answer already in place instead
+  // of momentarily rendering "no result" and then flipping to the win/lose
+  // box a moment later once this backstop catches up.
+  await checkLastRoundResult();
   refreshRound();
-  checkLastRoundResult();
   clearInterval(lastResultInterval);
   lastResultInterval = setInterval(checkLastRoundResult, 20000);
   clearInterval(roundTimerInterval);
@@ -906,6 +912,39 @@ async function withdraw() {
   refreshMe();
 }
 
+// Server push: an SSE channel that notifies the instant round/bet/balance
+// state changes anywhere (see app/rounds/events.py), instead of everyone
+// waiting for their next poll tick. The message carries no payload — it just
+// means "something changed", so we react by immediately re-running the same
+// refreshes the polling loop would eventually do on its own. Polling is left
+// completely in place as a fallback: if this connection is blocked/dropped
+// (proxy, browser setting, flaky network), the page keeps working exactly as
+// before, just without the instant nudge.
+let roundEventSource = null;
+
+function onRoundServerEvent() {
+  if (token) {
+    refreshRound();
+    refreshMe();
+    checkLastRoundResult();
+  } else {
+    refreshChainStatusOnly();
+  }
+}
+
+function connectRoundEvents() {
+  if (roundEventSource) return;
+  roundEventSource = new EventSource('/rounds/stream');
+  roundEventSource.addEventListener('update', onRoundServerEvent);
+  // Fires on the initial connection AND every successful auto-reconnect (the
+  // browser retries this on its own after a drop) — re-syncs immediately
+  // instead of leaving the page on whatever it last knew until the next event
+  // or poll tick, which would otherwise widen the "missed while disconnected"
+  // window to the full reconnect gap.
+  roundEventSource.addEventListener('open', onRoundServerEvent);
+}
+
+connectRoundEvents();
 initAuthState();
 </script>