fix: keep is_public and visibility in sync on updates

When visibility changes to 'public', is_public=True. When it changes away
from 'public', is_public=False. When is_public is set via TreeUpdate,
visibility column is updated to match.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

backend/app/api/endpoints/trees.py

@@ -629,6 +629,13 @@ async def update_tree(
     for field, value in update_data.items():
         setattr(tree, field, value)
 
+    # Keep visibility and is_public in sync
+    if tree_data.is_public is not None:
+        if tree_data.is_public and tree.visibility not in ('public',):
+            tree.visibility = 'public'
+        elif not tree_data.is_public and tree.visibility == 'public':
+            tree.visibility = 'team'  # downgrade from public to team
+
     # Increment version if tree structure changed
     if "tree_structure" in update_data:
         tree.version += 1
@@ -1074,6 +1081,7 @@ async def update_tree_visibility(
     # Update visibility
     old_visibility = tree.visibility
     tree.visibility = visibility_data.visibility
+    tree.is_public = (visibility_data.visibility == 'public')
 
     await log_audit(db, current_user.id, "tree.visibility.update", "tree", tree.id,
                     {"tree_name": tree.name, "old_visibility": old_visibility,