Implement asynchronous save manager with UI update optimizations and add tests for save functionality

tests/fixtures/ui_stage.gd

@@ -0,0 +1,14 @@
+extends "res://stage/stage.gd"
+
+# Keep scene wiring and display logic, without accessing the player's save.
+func load_data() -> bool:
+    return false
+
+func save_data() -> void:
+    pass
+
+func _process(_delta: float) -> void:
+    pass
+
+func _notification(_what: int) -> void:
+    pass

tests/fixtures/ui_stage.gd.uid

@@ -0,0 +1 @@
+uid://c8ewikdhlvnex