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/handler.go

@@ -245,6 +245,9 @@ func uiPrefsDTO(p UIPrefs) gen.UiPrefs {
 		WaveVariant:    (*gen.UiPrefsWaveVariant)(p.WaveVariant),
 		WebPlayer:      (*gen.UiPrefsWebPlayer)(p.WebPlayer),
 		SearchPosition: (*gen.UiPrefsSearchPosition)(p.SearchPos),
+		SearchCollapse: p.SearchFold,
+		HomeActivities: p.HomeActs,
+		HomeMoods:      p.HomeMoods,
 		MobilePlayer:   (*gen.UiPrefsMobilePlayer)(p.MobilePlayer),
 		Ambient:        p.Ambient,
 		CrossfadeS:     p.CrossfadeS,
@@ -258,6 +261,9 @@ func uiPrefsFromDTO(p gen.UiPrefs) UIPrefs {
 		WaveVariant:  (*string)(p.WaveVariant),
 		WebPlayer:    (*string)(p.WebPlayer),
 		SearchPos:    (*string)(p.SearchPosition),
+		SearchFold:   p.SearchCollapse,
+		HomeActs:     p.HomeActivities,
+		HomeMoods:    p.HomeMoods,
 		MobilePlayer: (*string)(p.MobilePlayer),
 		Ambient:      p.Ambient,
 		CrossfadeS:   p.CrossfadeS,