Rebuild the coach conversation surface so it uses the full width without
feeling cramped:
- Widen the inline history rail (260px -> 300px on lg, 340px on xl) and
bump rail typography + padding off the cramped 10/11px scale so the
conversation list and source toggles read at a comfortable size.
- Align the dividers across columns: the header, the history-rail
heading, and the centre rail-tray strip now share one fixed h-14 band
with identical borders, so the lines land on the same row instead of
the restless two-height split.
- Redesign the header leading cluster: the surface-toggle sits in its
own group behind a hairline divider rather than crowding the avatar,
which steps up to size-9.
- Give the full-page coach card more vertical room and a soft shadow so
it fills the standalone route instead of leaving a wasted band below.
- Even the coach FAB corner inset so the right gap matches the bottom
gap at each breakpoint.