### 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
return animation;
}
void AnimationTrackEditor::_root_removed() {
	root = nullptr;
}
void AnimationTrackEditor::set_root(Node *p_root) {
	if (root) {
		root->disconnect("tree_exiting", callable_mp(this, &AnimationTrackEditor::_root_removed));
	}
	root = p_root;
	if (root) {
		root->connect("tree_exiting", callable_mp(this, &AnimationTrackEditor::_root_removed), CONNECT_ONE_SHOT);
	}
	_update_tracks();
}
Node *AnimationTrackEditor::get_root() const {