Implement instant websocket room updates

.ai/rules/index.md

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+# Project Rules Index
+
+Before planning or editing, find the row whose globs match the file's path and read that rule file.
+
+| Applies to | Rule file |
+| --- | --- |
+| {app/Events/**,app/Services/Rooms/**,resources/js/composables/**} | .ai/rules/js-composables.md |

.ai/rules/js-composables.md

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+---
+paths:
+  - '{app/Events/**,app/Services/Rooms/**,resources/js/composables/**}'
+---
+
+# Js Composables
+
+## Never broadcast hidden room votes
+Room table updates are delivered as synchronous WebSocket state payloads without polling or Inertia reloads. Before a round is revealed, broadcast only has_voted and keep every player's vote null; actual vote values may enter the shared payload only after reveal. State-changing commands remain server-authorized HTTP requests.