### Godot version

4.1.rc2

### System information

MacOS 13.4.1

### Issue description

![image](https://github.com/godotengine/godot/assets/4489798/cf4d2074-7d8a-48d4-ba87-ba04d7f2dda1)
Scrollbar does not show when output values are provided after starting the game. Also, it does not scroll to the bottom automatically need to press the search button to show the scrollbar or any button that refreshes the output window.

### Steps to reproduce

1. Create a project
2. Run in _process function a `print()` with some values to output it in the `output window`
3. Turn the game on and off until the scrollbar stops appearing.

### Minimal reproduction project

[ScrollbarBug.zip](https://github.com/godotengine/godot/files/11924845/ScrollbarBug.zip)

switch (p_option) {
		case MENU_COPY: {
			selection_copy();
		} break;
		case MENU_SELECT_ALL: {
			select_all();
		} break;
	}
}
void RichTextLabel::_draw_fbg_boxes(RID p_ci, RID p_rid, Vector2 line_off, Item *it_from, Item *it_to, int start, int end, int fbg_flag) {