### 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)

int prev_expansion_rows = expansion_rows;
			expansion_rows = 0;
			const int bsize = (grid_size.height * 80 / 100) / 2;
			const int h = bsize * 2 + 1;
			Color color = get_theme_color(read_only ? SNAME("disabled_highlight_color") : SNAME("highlight_color"), SNAME("Editor"));
			Color text_color = get_theme_color(read_only ? SNAME("disabled_font_color") : SNAME("font_color"), SNAME("Editor"));
			text_color.a *= 0.5;
			Color text_color_on = get_theme_color(read_only ? SNAME("disabled_font_color") : SNAME("font_hover_color"), SNAME("Editor"));
			text_color_on.a *= 0.7;
			const int vofs = (grid_size.height - h) / 2;
			int layer_index = 0;
			Point2 arrow_pos;
			Point2 block_ofs(4, vofs);
			while (true) {
				Point2 ofs = block_ofs;
				for (int i = 0; i < 2; i++) {
					for (int j = 0; j < layer_group_size; j++) {
						const bool on = value & (1 << layer_index);
						Rect2 rect2 = Rect2(ofs, Size2(bsize, bsize));
						color.a = on ? 0.6 : 0.2;
						if (layer_index == hovered_index) {
							
							color.a += 0.15;
						}
						draw_rect(rect2, color);
						flag_rects.push_back(rect2);
						Ref<Font> font = get_theme_font(SNAME("font"), SNAME("Label"));
						int font_size = get_theme_font_size(SNAME("font_size"), SNAME("Label"));
						Vector2 offset;
						offset.y = rect2.size.y * 0.75;