fix: propagate client.start() errors to caller instead of swallowing

Codex review feedback: ensureSharedClientStarted now throws the error
from client.start() if it rejects during the 2s grace window, so
resolveSharedMatrixClient() properly reports failure (e.g. bad token,
unreachable homeserver) instead of leaving the provider in a
running-but-not-syncing state.

extensions/matrix/src/matrix/client/shared.ts

@@ -87,16 +87,19 @@ async function ensureSharedClientStarted(params: {
     // bot-sdk start() returns a promise that never resolves (infinite sync loop).
     // Fire-and-forget: the sync loop runs and events fire on the client,
     // but we must not await or the entire provider startup hangs forever.
-    let startFailed = false;
+    // If start() rejects during the grace window (e.g. bad token, unreachable
+    // homeserver), we propagate the error so the caller knows startup failed.
+    let startError: unknown = undefined;
     client.start().catch((err: unknown) => {
-      startFailed = true;
+      startError = err;
       LogService.error("MatrixClientLite", "client.start() error:", err);
     });
     // Give the sync loop a moment to initialize before marking ready
     await new Promise(resolve => setTimeout(resolve, 2000));
-    if (!startFailed) {
-      params.state.started = true;
+    if (startError) {
+      throw startError;
     }
+    params.state.started = true;
   })();
   sharedClientStartPromises.set(key, startPromise);
   try {