feat(web): settings to keep the search open and hide home pickers; collapsible menu sections

- appearance settings get "collapse search" (off keeps the field always open)
  and separate switches for the activity and mood pickers on the home page;
  stored in ui_prefs (search_collapse, home_activities, home_moods)
- Collection and Admin headers in the sidebar fold their items; the state is
  remembered in the browser, a folded Admin shows the review queue badge;
  icon-only and phone layouts always show every item

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

services/api/internal/auth/validate.go

@@ -135,6 +135,15 @@ func MergeUIPrefs(base, patch UIPrefs) UIPrefs {
 	if patch.SearchPos != nil {
 		base.SearchPos = patch.SearchPos
 	}
+	if patch.SearchFold != nil {
+		base.SearchFold = patch.SearchFold
+	}
+	if patch.HomeActs != nil {
+		base.HomeActs = patch.HomeActs
+	}
+	if patch.HomeMoods != nil {
+		base.HomeMoods = patch.HomeMoods
+	}
 	if patch.MobilePlayer != nil {
 		base.MobilePlayer = patch.MobilePlayer
 	}