[livemate] New Livemate Panel

[sbuggay]

Summary

This change adds a new experimental panel for AI integration with React Native.

Test plan

Needs a few other changes to test E2E. Panel can be toggled with the experimental flag Enable Livemate Panel.

• This change maintains backwards compatibility with previous Local Storage data (if modifying settings, experiments, or other persisted client state).

Upstreaming plan

• This commit should be sent as a patch to the upstream devtools-frontend repo following the contribution guide for Meta employees OR contribution guide.
• This commit is React Native-specific and cannot be upstreamed.