A no-login directory of shared trees, backed by GET /api/v1/public/trees:
- /explore: searchable grid of public trees; debounced name search. Because the
backend adds `site_members` trees when a valid session is present, signed-in
users see more with no client-side branching.
- PublicHeader extracted and shared by /p and /explore (logo, Explore, Sign in).
- "Explore" entry added to the authed sidebar.
tsc clean; next build passes.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Signed-off-by: Justin Paul <justin@jpaul.me>