### Tested versions

Godot Engine v4.2.stable.official.46dc27791

### System information

Windows 10

### Issue description

When exporting to web, Godot fails with this error in the console:

> scene/main/window.cpp:884 - Attempting to make child window exclusive, but the parent window already has another exclusive child. This window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->VBoxContainer@<!-- -->137/@<!-- -->AcceptDialog@<!-- -->411, parent window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559, current exclusive child window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->ProgressDialog@<!-- -->17444

![a](https://github.com/godotengine/godot/assets/2000051/bf9d22aa-d3fe-4e11-bff6-c387e740fe90)

This happens for newly created empty projects.


### Steps to reproduce

1. Open the attached project (or create a new project).
2. Project->Export->Export All
3. Observe the console error.  No output files are generated.


### Minimal reproduction project (MRP)

[export_test.zip](https://github.com/godotengine/godot/files/13574810/export_test.zip)

p_log->add_image(p_log->get_editor_theme_icon(SNAME("StatusError")), 16 * EDSCALE, 16 * EDSCALE, Color(1.0, 1.0, 1.0), INLINE_ALIGNMENT_CENTER);
		p_log->add_text(" ");
		p_log->add_text(TTR("Failed."));
		has_messages = true;
	}
	p_log->add_newline();
	if (msg_count) {
		p_log->push_table(2);
		p_log->set_table_column_expand(0, false);
		p_log->set_table_column_expand(1, true);
		for (int m = 0; m < msg_count; m++) {
			EditorExportPlatform::ExportMessage msg = get_message(m);
			Color color = p_log->get_theme_color(SNAME("font_color"), SNAME("Label"));
			Ref<Texture> icon;
			switch (msg.msg_type) {
				case EditorExportPlatform::EXPORT_MESSAGE_INFO: {
					color = p_log->get_theme_color(SNAME("font_color"), EditorStringName(Editor)) * Color(1, 1, 1, 0.6);
				} break;
				case EditorExportPlatform::EXPORT_MESSAGE_WARNING: {
					icon = p_log->get_editor_theme_icon(SNAME("Warning"));
					color = p_log->get_theme_color(SNAME("warning_color"), EditorStringName(Editor));
				} break;
				case EditorExportPlatform::EXPORT_MESSAGE_ERROR: {
					icon = p_log->get_editor_theme_icon(SNAME("Error"));
					color = p_log->get_theme_color(SNAME("error_color"), EditorStringName(Editor));
				} break;
				default:
					break;
			}
			p_log->push_cell();