### 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)

ProjectSettings::get_singleton()->set_setting(setting_identifier, true);
	ProjectSettings::get_singleton()->save();
	EditorFileSystem::get_singleton()->scan_changes();
	emit_signal("texture_format_enabled");
}
void ProjectExportTextureFormatError::_bind_methods() {
	ADD_SIGNAL(MethodInfo("texture_format_enabled"));
}
void ProjectExportTextureFormatError::_notification(int p_what) {
	switch (p_what) {
		case NOTIFICATION_THEME_CHANGED: {
			texture_format_error_label->add_theme_color_override("font_color", get_theme_color(SNAME("error_color"), EditorStringName(Editor)));
		} break;
	}
}
void ProjectExportTextureFormatError::show_for_texture_format(const String &p_friendly_name, const String &p_setting_identifier) {
	texture_format_error_label->set_text(vformat(TTR("Target platform requires '%s' texture compression. Enable 'Import %s' to fix."), p_friendly_name, p_friendly_name.replace("/", " ")));
	setting_identifier = p_setting_identifier;
	show();
}
ProjectExportTextureFormatError::ProjectExportTextureFormatError() {