fix: stop tmux observer from blinking the main observation badge
Both desktop and tmux observers emit observe.status events. The health
page was updating state.observe.mode from all events unconditionally,
so the badge alternated between "Recording" (desktop, mode=screencast)
and "Tmux" (tmux observer, mode=tmux) with every heartbeat.
The tmux sub-observer's mode is informational for its remote card only.
Only update the main mode badge from events that don't carry msg.tmux
(i.e., from the primary desktop observer).
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>