feat(web): add WebSocket transport for message event streaming with SSE fallback (#764)

* feat: add websocket message stream transport

* fix: avoid false missing session directories in sidebar

* fix: re-probe project root session directories

* refactor: use button group for message stream transport

* fix: resolve chat input hook dependency warning

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Co-authored-by: Bohdan Triapitsyn <artmore@protonmail.com>

packages/ui/src/lib/api/types.ts

@@ -569,6 +569,7 @@ export interface SettingsPayload {
   showExpandedBashTools?: boolean;
   showExpandedEditTools?: boolean;
   chatRenderMode?: 'sorted' | 'live';
+  messageStreamTransport?: 'auto' | 'ws' | 'sse';
   activityRenderMode?: 'collapsed' | 'summary';
   mermaidRenderingMode?: 'svg' | 'ascii';
   fontSize?: number;