### 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
ERR_FAIL_COND(plugin_init_callback_count == MAX_INIT_CALLBACKS);
	plugin_init_callbacks[plugin_init_callback_count++] = p_callback;
}
EditorPluginInitializeCallback EditorNode::plugin_init_callbacks[EditorNode::MAX_INIT_CALLBACKS];
int EditorNode::build_callback_count = 0;
void EditorNode::add_build_callback(EditorBuildCallback p_callback) {
	ERR_FAIL_COND(build_callback_count == MAX_INIT_CALLBACKS);
	build_callbacks[build_callback_count++] = p_callback;
}
EditorBuildCallback EditorNode::build_callbacks[EditorNode::MAX_BUILD_CALLBACKS];
bool EditorNode::call_build() {
	bool builds_successful = true;
	for (int i = 0; i < build_callback_count && builds_successful; i++) {
		if (!build_callbacks[i]()) {
			ERR_PRINT("A Godot Engine build callback failed.");
			builds_successful = false;
		}
	}
	if (builds_successful && !editor_data.call_build()) {
		ERR_PRINT("An EditorPlugin build callback failed.");
		builds_successful = false;
	}
	return builds_successful;
}
void EditorNode::_inherit_imported(const String &p_action) {
	open_imported->hide();
	load_scene(open_import_request, true, true);
}
void EditorNode::_open_imported() {