### 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)

}
				gloff.x += glyphs[i].advance;
			}
		}
		Vector2 fbg_line_off = off + p_ofs;
		
		Vector2i chr_range = TS->shaped_text_get_range(rid);
		_draw_fbg_boxes(ci, rid, fbg_line_off, it_from, it_to, chr_range.x, chr_range.y, 0);
		
		Color selection_bg = theme_cache.selection_color;
		int sel_start = -1;
		int sel_end = -1;
		if (selection.active && (selection.from_frame->lines[selection.from_line].char_offset + selection.from_char) <= (l.char_offset + TS->shaped_text_get_range(rid).y) && (selection.to_frame->lines[selection.to_line].char_offset + selection.to_char) >= (l.char_offset + TS->shaped_text_get_range(rid).x)) {
			sel_start = MAX(TS->shaped_text_get_range(rid).x, (selection.from_frame->lines[selection.from_line].char_offset + selection.from_char) - l.char_offset);
			sel_end = MIN(TS->shaped_text_get_range(rid).y, (selection.to_frame->lines[selection.to_line].char_offset + selection.to_char) - l.char_offset);
			Vector<Vector2> sel = TS->shaped_text_get_selection(rid, sel_start, sel_end);
			for (int i = 0; i < sel.size(); i++) {
				Rect2 rect = Rect2(sel[i].x + p_ofs.x + off.x, p_ofs.y + off.y - TS->shaped_text_get_ascent(rid), sel[i].y - sel[i].x, TS->shaped_text_get_size(rid).y);
				RenderingServer::get_singleton()->canvas_item_add_rect(ci, rect, selection_bg);
			}
		}
		Vector2 ul_start;
		bool ul_started = false;
		Color ul_color;
		Vector2 dot_ul_start;
		bool dot_ul_started = false;
		Color dot_ul_color;
		Vector2 st_start;
		bool st_started = false;
		Color st_color;