### Godot version

v4.0.alpha11.official [afdae67cc] (when the feature was added) and newer (still happens in RC6)

### System information

Windows 10

### Issue description

I'm unable to handle when the user sets an exported node property (this feature: https://github.com/godotengine/godot/pull/62185) from a setter in the editor (tool script).

I don't know if this is intentional or not, but for me it was unexpected. I had to revert back to `NodePath`s.

### Steps to reproduce

- Create a scene
- Attach a script to a node
- Add `@tool` at the top of the script
- Export a node property with a setter, preferably with an easy way to see if it executed:
	```
	@export var node:Node:
		set (mod_value):
			prints("node", mod_value)
			node = mod_value
	```
- Save, close and open again the scene to make sure the tool script is running in the editor
- Set the node property from the inspector
- Observe that the setter didn't run

The setter is not bypassed when running the game, it is only bypassed in the editor.

We can compare with a `NodePath` property, which setter is not bypassed regardless if it is in the editor or in game runtime.

### Minimal reproduction project

[nodepath.zip](https://github.com/godotengine/godot/files/10840411/nodepath.zip)

draw_string(font, rect2.position + offset, itos(layer_index + 1), HORIZONTAL_ALIGNMENT_CENTER, rect2.size.x, font_size, on ? text_color_on : text_color);
						ofs.x += bsize + 1;
						++layer_index;
					}
					ofs.x = block_ofs.x;
					ofs.y += bsize + 1;
				}
				if (layer_index >= layer_count) {
					if (!flag_rects.is_empty() && (expansion_rows == 0)) {
						const Rect2 &last_rect = flag_rects[flag_rects.size() - 1];
						arrow_pos = last_rect.get_end();
					}
					break;
				}
				int block_size_x = layer_group_size * (bsize + 1);
				block_ofs.x += block_size_x + 3;
				if (block_ofs.x + block_size_x + 12 > grid_size.width) {
					
					if (!flag_rects.is_empty() && (expansion_rows == 0)) {
						const Rect2 &last_rect = flag_rects[flag_rects.size() - 1];
						arrow_pos = last_rect.get_end();
					}
					++expansion_rows;
					if (expanded) {
						
						block_ofs.x = 4;
						block_ofs.y += 2 * (bsize + 1) + 3;
					} else {
						
						break;