### 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
int key_idx = -1;
		float key_distance = 1e20;
		
		for (int i = animation->track_get_key_count(track) - 1; i >= 0; i--) {
			Rect2 rect = const_cast<AnimationTrackEdit *>(this)->get_key_rect(i, timeline->get_zoom_scale());
			float offset = animation->track_get_key_time(track, i) - timeline->get_value();
			offset = offset * timeline->get_zoom_scale() + limit;
			rect.position.x += offset;
			if (rect.has_point(p_pos)) {
				if (const_cast<AnimationTrackEdit *>(this)->is_key_selectable_by_distance()) {
					float distance = ABS(offset - p_pos.x);
					if (key_idx == -1 || distance < key_distance) {
						key_idx = i;
						key_distance = distance;
					}
				} else {
					
					break;
				}
			}
		}
		if (key_idx != -1) {
			String text = TTR("Time (s):") + " " + TS->format_number(rtos(Math::snapped(animation->track_get_key_time(track, key_idx), 0.0001))) + "\n";
			switch (animation->track_get_type(track)) {
				case Animation::TYPE_POSITION_3D: {
					Vector3 t = animation->track_get_key_value(track, key_idx);
					text += TTR("Position:") + " " + String(t) + "\n";
				} break;
				case Animation::TYPE_ROTATION_3D: {
					Quaternion t = animation->track_get_key_value(track, key_idx);