### 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)

if (column == col_count - 1 || E->next() == nullptr) {
						offset.x = 0;
						row_height += theme_cache.table_v_separation;
						table->total_height += row_height;
						offset.y += row_height;
						table->rows.push_back(row_height);
						table->rows_baseline.push_back(table->total_height - row_height + row_baseline);
						row_height = 0;
					}
					idx++;
				}
				int row_idx = (table->align_to_row < 0) ? table->rows_baseline.size() - 1 : table->align_to_row;
				if (table->rows_baseline.size() != 0 && row_idx < (int)table->rows_baseline.size() - 1) {
					l.text_buf->add_object((uint64_t)it, Size2(table->total_width, table->total_height), table->inline_align, t_char_count, Math::round(table->rows_baseline[row_idx]));
				} else {
					l.text_buf->add_object((uint64_t)it, Size2(table->total_width, table->total_height), table->inline_align, t_char_count);
				}
				txt += String::chr(0xfffc).repeat(t_char_count);
			} break;
			default:
				break;
		}
	}
	
	l.text_buf->set_bidi_override(structured_text_parser(_find_stt(l.from), st_args, txt));
	*r_char_offset = l.char_offset + l.char_count;
	l.offset.y = p_h;
	return _calculate_line_vertical_offset(l);
}
int RichTextLabel::_draw_line(ItemFrame *p_frame, int p_line, const Vector2 &p_ofs, int p_width, const Color &p_base_color, int p_outline_size, const Color &p_outline_color, const Color &p_font_shadow_color, int p_shadow_outline_size, const Point2 &p_shadow_ofs, int &r_processed_glyphs) {