### 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)

for (int i = 0; i < 12; i++) {
		spin[i]->set_min(p_min);
		spin[i]->set_max(p_max);
		spin[i]->set_step(p_step);
		spin[i]->set_hide_slider(p_hide_slider);
		spin[i]->set_allow_greater(true);
		spin[i]->set_allow_lesser(true);
		if (i % 4 == 3) {
			spin[i]->set_suffix(p_suffix);
		}
	}
}
EditorPropertyTransform3D::EditorPropertyTransform3D() {
	GridContainer *g = memnew(GridContainer);
	g->set_columns(4);
	add_child(g);
	static const char *desc[12] = { "xx", "xy", "xz", "xo", "yx", "yy", "yz", "yo", "zx", "zy", "zz", "zo" };
	for (int i = 0; i < 12; i++) {
		spin[i] = memnew(EditorSpinSlider);
		spin[i]->set_label(desc[i]);
		spin[i]->set_flat(true);
		g->add_child(spin[i]);
		spin[i]->set_h_size_flags(SIZE_EXPAND_FILL);
		add_focusable(spin[i]);
		spin[i]->connect("value_changed", callable_mp(this, &EditorPropertyTransform3D::_value_changed).bind(desc[i]));
	}
	set_bottom_editor(g);
}
void EditorPropertyProjection::_set_read_only(bool p_read_only) {