fix: avoid false crash alert for shared browser handoff

[atomantic]

Summary

• Keep the intentional shared-CDP browser handoff in the foreground through tab opening.
• Add a short grace period so PM2 does not classify its clean exit as an unstable restart.
• Preserve the existing own-Chrome fallback, including real failure visibility.

Test plan

• bash -n .browser/start.sh
• npm run check:file-sizes
• Synthetic PM2 handoff: stopped with exit 0 and unstable_restarts: 0
• npm run build and npm run test:unit attempted; the checkout lacks the declared pg dependency, with 146 other unit tests passing.