### 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)

#endif
	export_button->connect("pressed", callable_mp(this, &ProjectExportDialog::_export_project));
	// 
	export_button->set_disabled(true);
	export_all_dialog = memnew(ConfirmationDialog);
	add_child(export_all_dialog);
	export_all_dialog->set_title(TTR("Export All"));
	export_all_dialog->set_text(TTR("Choose an export mode:"));
	export_all_dialog->get_ok_button()->hide();
	export_all_dialog->add_button(TTR("Debug"), true, "debug");
	export_all_dialog->add_button(TTR("Release"), true, "release");
	export_all_dialog->connect("custom_action", callable_mp(this, &ProjectExportDialog::_export_all_dialog_action));
#ifdef ANDROID_ENABLED
	export_all_dialog->hide();
	export_all_button = memnew(Button);
	export_all_button->hide();
#else
	export_all_button = add_button(TTR("Export All..."), !DisplayServer::get_singleton()->get_swap_cancel_ok(), "export");
#endif
	export_all_button->connect("pressed", callable_mp(this, &ProjectExportDialog::_export_all_dialog));
	export_all_button->set_disabled(true);
	export_pck_zip = memnew(EditorFileDialog);
	export_pck_zip->add_filter("*.zip", TTR("ZIP File"));
	export_pck_zip->add_filter("*.pck", TTR("Godot Project Pack"));
	export_pck_zip->set_access(EditorFileDialog::ACCESS_FILESYSTEM);
	export_pck_zip->set_file_mode(EditorFileDialog::FILE_MODE_SAVE_FILE);
	add_child(export_pck_zip);
	export_pck_zip->connect("file_selected", callable_mp(this, &ProjectExportDialog::_export_pck_zip_selected));
	// 
	export_texture_format_error = memnew(ProjectExportTextureFormatError);