### 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 i = 0; i < track_len; i++) {
				bool do_bake = false;
				Animation::TrackType type = animation->track_get_type(i);
				do_bake |= b_trs && (type == Animation::TYPE_POSITION_3D || type == Animation::TYPE_ROTATION_3D || type == Animation::TYPE_SCALE_3D);
				do_bake |= b_bs && type == Animation::TYPE_BLEND_SHAPE;
				do_bake |= b_v && type == Animation::TYPE_VALUE;
				if (do_bake && !animation->track_is_compressed(i)) {
					Animation::InterpolationType it = animation->track_get_interpolation_type(i);
					if (it == Animation::INTERPOLATION_NEAREST) {
						continue; 
					}
					
					bool is_using_angle = it == Animation::INTERPOLATION_LINEAR_ANGLE || it == Animation::INTERPOLATION_CUBIC_ANGLE;
					
					Vector<Pair<real_t, Variant>> insert_queue_new;
					switch (type) {
						case Animation::TYPE_POSITION_3D: {
							for (double delta_t = 0.0; delta_t <= anim_len; delta_t += dur_step) {
								Pair<real_t, Variant> keydata;
								keydata.first = delta_t;
								Vector3 v;
								animation->try_position_track_interpolate(i, delta_t, &v);
								keydata.second = v;
								insert_queue_new.append(keydata);
							}
						} break;
						case Animation::TYPE_ROTATION_3D: {
							for (double delta_t = 0.0; delta_t <= anim_len; delta_t += dur_step) {
								Pair<real_t, Variant> keydata;
								keydata.first = delta_t;