### Godot version

4.0.dev

### System information

win11，core i7 13700,  GTX4090

### Issue description

Just look at this gif.

![screenshots](https://user-images.githubusercontent.com/1620585/225354749-6ea17059-95b2-45e0-9765-8505e92726eb.gif)

It seems that it was block by Static Type Checking.

![image](https://user-images.githubusercontent.com/1620585/225362874-507ff0ec-c6d8-4a25-9a16-89db1885ad02.png)

If it's right.

Why it doesn't just disable other option except for String and StringName?

### Steps to reproduce

1. first select string type
2. input a text
3. change type
4. change back to string  -- it don't work
5. change to stringname -- it works
6. change back to string -- it works

### Minimal reproduction project

I think it don't need reproduction project.
NodePath np = value;
	if (np == NodePath()) {
		return;
	}
	Node *root = EditorNode::get_singleton()->get_tree()->get_root();
	Node *np_node = root->get_node(np);
	ERR_FAIL_COND(!np_node);
	Node *edited_node = root->get_node(base);
	ERR_FAIL_COND(!edited_node);
	value = edited_node->get_path_to(np_node);
}
void AnimationTrackKeyEdit::_update_obj(const Ref<Animation> &p_anim) {
	if (setting || animation != p_anim) {
		return;
	}
	notify_change();
}
void AnimationTrackKeyEdit::_key_ofs_changed(const Ref<Animation> &p_anim, float from, float to) {
	if (animation != p_anim || from != key_ofs) {
		return;
	}
	key_ofs = to;
	if (setting) {
		return;
	}
	notify_change();
}
bool AnimationTrackKeyEdit::_set(const StringName &p_name, const Variant &p_value) {