### Godot version

4.2.dev3.official

### System information

Godot v4.2.dev3 - Windows 10.0.19045 - GLES3 (Compatibility)

### Issue description

The toggle button "Show Built-In Actions" in the "Input Map" tab of the Project Settings window does not keep its ON state after restarting the editor - it always resets to being OFF.

This is different than the behaviour of the "Advanced Settings" toggle button in the "General" tab of the Project Settings - this one does keep its state between editor restarts.

I'm not sure if what I am reporting is an issue or the intended behaviour.

### Steps to reproduce

1. Create a new project.
2. Go to Project -> Project Settings -> Input Map and toggle "Show Built-In Actions" button to ON.
3. Restart the Godot editor.
4. Check if the setting was kept or changed.

### Minimal reproduction project

N/A
TreeItem *item = action_tree->get_selected();
	if (!item || !item->has_meta("__event")) {
		return;
	}
	_tree_button_pressed(item, 2, BUTTON_EDIT_EVENT, MouseButton::LEFT);
}
void ActionMapEditor::set_show_builtin_actions(bool p_show) {
	show_builtin_actions = p_show;
	show_builtin_actions_checkbutton->set_pressed(p_show);
	
	if (!actions_cache.is_empty()) {
		update_action_list();
	}
}
void ActionMapEditor::_search_term_updated(const String &) {