### Godot version

4.0.stable

### System information

Windows 10, Forward+, GTX 1070 driver 528.49

### Issue description

When trying to edit the handle mode of a bezier cruve key from the inspector tab, the mode doesn't change. It works fine when right clicking on the key and setting the handle mode from here though. 

https://user-images.githubusercontent.com/24484962/222379540-29d71b6d-ff0c-4a21-9905-9750d0581fda.mp4



### Steps to reproduce

On an animation track using a bezier curve, select a key and try to change the handle mode from the inspector tab

### Minimal reproduction project

N/A
ERR_FAIL_NULL(root);
	Node *node = get_node(p_path);
	ERR_FAIL_NULL(node);
	NodePath path_to = root->get_path_to(node, true);
	if (adding_track_type == Animation::TYPE_BLEND_SHAPE && !node->is_class("MeshInstance3D")) {
		EditorNode::get_singleton()->show_warning(TTR("Blend Shape tracks only apply to MeshInstance3D nodes."));
		return;
	}
	if ((adding_track_type == Animation::TYPE_POSITION_3D || adding_track_type == Animation::TYPE_ROTATION_3D || adding_track_type == Animation::TYPE_SCALE_3D) && !node->is_class("Node3D")) {
		EditorNode::get_singleton()->show_warning(TTR("Position/Rotation/Scale 3D tracks only apply to 3D-based nodes."));
		return;
	}
	switch (adding_track_type) {
		case Animation::TYPE_VALUE: {
			adding_track_path = path_to;
			prop_selector->set_type_filter(Vector<Variant::Type>());
			prop_selector->select_property_from_instance(node);
		} break;
		case Animation::TYPE_BLEND_SHAPE: {
			adding_track_path = path_to;
			Vector<Variant::Type> filter;
			filter.push_back(Variant::FLOAT);
			prop_selector->set_type_filter(filter);
			prop_selector->select_property_from_instance(node);
		} break;
		case Animation::TYPE_POSITION_3D:
		case Animation::TYPE_ROTATION_3D:
		case Animation::TYPE_SCALE_3D:
		case Animation::TYPE_METHOD: {
			EditorUndoRedoManager *undo_redo = EditorUndoRedoManager::get_singleton();