### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
if (_initializing_plugins) {
		return;
	}
	Vector<String> enabled_addons;
	for (const KeyValue<String, EditorPlugin *> &E : addon_name_to_plugin) {
		enabled_addons.push_back(E.key);
	}
	if (enabled_addons.size() == 0) {
		ProjectSettings::get_singleton()->set("editor_plugins/enabled", Variant());
	} else {
		enabled_addons.sort();
		ProjectSettings::get_singleton()->set("editor_plugins/enabled", enabled_addons);
	}
	project_settings_editor->queue_save();
}
void EditorNode::set_addon_plugin_enabled(const String &p_addon, bool p_enabled, bool p_config_changed) {
	String addon_path = p_addon;
	if (!addon_path.begins_with("res:")) {
		addon_path = "res:addons/" + addon_path + "/plugin.cfg";
	}
	ERR_FAIL_COND(p_enabled && addon_name_to_plugin.has(addon_path));
	ERR_FAIL_COND(!p_enabled && !addon_name_to_plugin.has(addon_path));
	if (!p_enabled) {
		EditorPlugin *addon = addon_name_to_plugin[addon_path];
		remove_editor_plugin(addon, p_config_changed);
		memdelete(addon);
		addon_name_to_plugin.erase(addon_path);
		_update_addon_config();
		return;