### 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
for (int j = 0; j < track_edit_plugins.size(); j++) {
				track_edit = track_edit_plugins.write[j]->create_audio_track_edit();
				if (track_edit) {
					break;
				}
			}
		}
		if (animation->track_get_type(i) == Animation::TYPE_ANIMATION) {
			NodePath path = animation->track_get_path(i);
			Node *node = nullptr;
			if (root && root->has_node(path)) {
				node = root->get_node(path);
			}
			if (node && Object::cast_to<AnimationPlayer>(node)) {
				for (int j = 0; j < track_edit_plugins.size(); j++) {
					track_edit = track_edit_plugins.write[j]->create_animation_track_edit(node);
					if (track_edit) {
						break;
					}
				}
			}
		}
		if (track_edit == nullptr) {
			
			track_edit = memnew(AnimationTrackEdit);
		}
		track_edits.push_back(track_edit);
		if (use_grouping) {
			String base_path = animation->track_get_path(i);
			base_path = base_path.get_slice(":", 0);