fix: pair-agent server dies 15s after CLI exits

The server monitors BROWSE_PARENT_PID and self-terminates when the
parent exits. For pair-agent, the connect subprocess is the parent,
so the server dies 15s after connect finishes. Disable parent-PID
monitoring for pair-agent sessions so the server outlives the CLI.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

browse/src/cli.ts

@@ -839,6 +839,11 @@ Refs:           After 'snapshot', use @e1, @e2... as selectors:
         BROWSE_PORT: '34567',
         BROWSE_SIDEBAR_CHAT: '1',
       };
+      // If parent explicitly set BROWSE_PARENT_PID=0 (pair-agent disabling
+      // self-termination), pass it through so startServer doesn't override it.
+      if (process.env.BROWSE_PARENT_PID === '0') {
+        serverEnv.BROWSE_PARENT_PID = '0';
+      }
       const newState = await startServer(serverEnv);
 
       // Print connected status
@@ -975,7 +980,9 @@ Refs:           After 'snapshot', use @e1, @e2... as selectors:
       const connectProc = Bun.spawn([browseBin, 'connect'], {
         cwd: process.cwd(),
         stdio: ['ignore', 'inherit', 'inherit'],
-        env: process.env,
+        // Disable parent-PID monitoring: pair-agent needs the server to outlive
+        // the connect subprocess. Setting to 0 tells the server not to self-terminate.
+        env: { ...process.env, BROWSE_PARENT_PID: '0' },
       });
       await connectProc.exited;
       // Re-read state after headed mode switch