improve current session id message selectivity

[vzaidman]

Summary

The whole message was selected on click, instead of only the session-id.

Test plan

• 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. I've reviewed the contribution guide.
• This commit is React Native-specific and cannot be upstreamed.