client: Store `ReleaseChannel` instead of `&'static str` (#47868)

Closes #ISSUE

Store `ReleaseChannel` instead of `&'static str`. This allows displaying
other aspects about the channel than just the display name. Makes it
more concrete what is stored within the field, as it has limited
variants, as opposed to something like `session_id`

Release Notes:

- N/A *or* Added/Fixed/Improved ...
c3fddcd593tidely committed on 1/28/2026, 4:52:34 PM· committed by GitHubparent5e0b8cc
1 file changedLine totals unavailable