### 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)

export_all_dialog->hide();
	_export_all(p_str != "release");
}
void ProjectExportDialog::_export_all(bool p_debug) {
	String export_target = p_debug ? TTR("Debug") : TTR("Release");
	EditorProgress ep("exportall", TTR("Exporting All") + " " + export_target, EditorExport::get_singleton()->get_export_preset_count(), true);
	exporting = true;
	bool show_dialog = false;
	result_dialog_log->clear();
	for (int i = 0; i < EditorExport::get_singleton()->get_export_preset_count(); i++) {
		Ref<EditorExportPreset> preset = EditorExport::get_singleton()->get_export_preset(i);
		if (preset.is_null()) {
			exporting = false;
			ERR_FAIL_MSG("Failed to start the export: one of the presets is invalid.");
		}
		Ref<EditorExportPlatform> platform = preset->get_platform();
		if (platform.is_null()) {
			exporting = false;
			ERR_FAIL_MSG("Failed to start the export: one of the presets has no valid platform.");
		}
		ep.step(preset->get_name(), i);
		platform->clear_messages();
		Error err = platform->export_project(preset, p_debug, preset->get_export_path(), 0);
		if (err == ERR_SKIP) {
			exporting = false;
			return;
		}
		bool has_messages = platform->fill_log_messages(result_dialog_log, err);
		show_dialog = show_dialog || has_messages;
	}