### 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
String base = animation->get_path().substr(0, srpos);
			if (ResourceLoader::get_resource_type(base) == "PackedScene") {
				if (!get_tree()->get_edited_scene_root() || get_tree()->get_edited_scene_root()->get_scene_file_path() != base) {
					file_read_only = true;
				}
			} else {
				if (FileAccess::exists(base + ".import")) {
					file_read_only = true;
				}
			}
		}
	} else {
		if (FileAccess::exists(animation->get_path() + ".import")) {
			file_read_only = true;
		}
	}
	RBMap<String, VBoxContainer *> group_sort;
	bool use_grouping = !view_group->is_pressed();
	bool use_filter = selected_filter->is_pressed();
	for (int i = 0; i < animation->get_track_count(); i++) {
		AnimationTrackEdit *track_edit = nullptr;
		
		if (use_filter) {
			NodePath path = animation->track_get_path(i);
			if (root && root->has_node(path)) {
				Node *node = root->get_node(path);
				if (!node) {
					continue; 
				}
				if (!EditorNode::get_singleton()->get_editor_selection()->is_selected(node)) {