The manager that holds widgets is the WidgetManager

UIManager named the category, not the contents. Every other manager is
named after what it registers — ItemManager holds Items, SceneManager
holds Scenes — so the one that registers Widgets is the WidgetManager.

The alias, the Game field and both manual pages move together.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

core.game.go

@@ -21,7 +21,7 @@ type Game struct {
 	ScriptManager    *ScriptManager
 	AssetManager     *AssetManager
 	VerbManager      *VerbManager
-	UIManager        *UIManager
+	WidgetManager    *WidgetManager
 	ThemeManager     *ThemeManager
 
 	// SceneRect is the part of the window the picture occupies. Zero means
@@ -131,7 +131,7 @@ func NewGame(title string, w, h int) *Game {
 		ScriptManager:    NewManager[Script](),
 		AssetManager:     NewManager[Asset](),
 		VerbManager:      NewManager[Verb](),
-		UIManager:        NewManager[Widget](),
+		WidgetManager:    NewManager[Widget](),
 		ThemeManager:     NewManager[Theme](),
 		State:            NewState(),
 		Inventory:        NewInventory(),