fix(browse): server persists across Claude Code Bash calls

[joelgreen]

Problem

The browse server dies between Bash tool invocations in Claude Code. Every new $B command starts a fresh server, losing all cookies, page state, and navigation. This makes multi-step QA testing impossible.

Root cause: Two mechanisms kill the server when the parent Bash shell exits:

1. SIGTERM from sandbox: Claude Code's Bash tool sends SIGTERM to all child processes when a command completes. The server's SIGTERM handler called shutdown().

2. Parent PID watchdog: The server polls BROWSE_PARENT_PID every 15s. When the parent shell dies, the watchdog called shutdown().

Fix

• SIGTERM: log and ignore instead of shutdown(). Explicit shutdown still available via /stop or SIGINT.
• Parent watchdog: log once and continue instead of shutdown(). Idle timeout (30 min) handles cleanup.

What doesn't change

• /stop command and SIGINT still work for intentional shutdown
• Windows behavior unchanged
• Idle timeout still cleans up abandoned servers
• State file lifecycle unchanged

Repro (before fix)

# Call 1
$B goto http://localhost:3000/login
$B fill '#email' 'test@test.com'

# Call 2 (new Bash invocation)
$B url    # → "about:blank" (server restarted, state lost)

After fix

# Call 2 reconnects to existing server
$B url    # → "http://localhost:3000/login" (state preserved)

Verified across 5+ separate Bash calls maintaining cookies, form fields, and navigation.

[garrytan]

Thanks @joelgreen! Landing this in wave PR #1028 (v0.18.1.0). Closing here. 🚀