fix(browser): tolerate brief extension relay disconnects on attached tabs

Keep extension relay tab metadata available across short extension worker drops and allow CDP clients to connect while waiting for reconnect. This prevents false "no tab connected" failures in environments where the extension worker disconnects transiently (e.g. WSLg/MV3).

src/browser/extension-relay.test.ts

@@ -392,6 +392,53 @@ describe("chrome extension relay server", () => {
     ext2.close();
   });
 
+  it("keeps /json/version websocket endpoint during short extension disconnects", async () => {
+    const { port, ext } = await startRelayWithExtension();
+    ext.send(
+      JSON.stringify({
+        method: "forwardCDPEvent",
+        params: {
+          method: "Target.attachedToTarget",
+          params: {
+            sessionId: "cb-tab-disconnect",
+            targetInfo: {
+              targetId: "t-disconnect",
+              type: "page",
+              title: "Disconnect test",
+              url: "https://example.com",
+            },
+            waitingForDebugger: false,
+          },
+        },
+      }),
+    );
+
+    await waitForListMatch(
+      async () =>
+        (await fetch(`${cdpUrl}/json/list`, {
+          headers: relayAuthHeaders(cdpUrl),
+        }).then((r) => r.json())) as Array<{ id?: string }>,
+      (list) => list.some((entry) => entry.id === "t-disconnect"),
+    );
+
+    const extClosed = waitForClose(ext, 2_000);
+    ext.close();
+    await extClosed;
+
+    const version = (await fetch(`${cdpUrl}/json/version`, {
+      headers: relayAuthHeaders(cdpUrl),
+    }).then((r) => r.json())) as {
+      webSocketDebuggerUrl?: string;
+    };
+    expect(String(version.webSocketDebuggerUrl ?? "")).toContain("/cdp");
+
+    const cdp = new WebSocket(`ws://127.0.0.1:${port}/cdp`, {
+      headers: relayAuthHeaders(`ws://127.0.0.1:${port}/cdp`),
+    });
+    await waitForOpen(cdp);
+    cdp.close();
+  });
+
   it("waits briefly for extension reconnect before failing CDP commands", async () => {
     const { port, ext: ext1 } = await startRelayWithExtension();
     const cdp = new WebSocket(`ws://127.0.0.1:${port}/cdp`, {