fix(#212, #378, #395): lifecycle and shutdown improvements

[giulio-leone]

Lifecycle & Shutdown Improvements

Grouped fix for three related lifecycle/shutdown issues.

Changes

#212 — Check browser connection in isLaunched()

• isLaunched() now calls browser.isConnected() instead of just checking browser !== null
• Also checks persistent context state so manually-closed browsers are detected correctly

#378 — Prevent hanging Chrome processes on shutdown

• Reworked shutdown flow in src/daemon.ts with a shuttingDown guard to prevent re-entrant cleanup
• Added 1 s close timeout → 5 s force-exit fallback to ensure the process never hangs
• Graceful shutdown kills browser contexts before force-terminating

#395 — Flush stdout before exit to prevent terminal freeze

• Introduced flush_and_exit() in Rust CLI (cli/src/main.rs) that flushes stdout before calling exit()
• When stdout is piped (e.g. from Claude Code), full buffering can cause the caller to hang; flushing prevents this

Files Changed

File	Issue
src/browser.ts	#212
src/daemon.ts	#378
cli/src/main.rs	#395

Testing

• npx tsc --noEmit — passes
• cargo check (cli) — passes

Closes #212, closes #378, closes #395

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