### 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)

ERR_FAIL_INDEX_V(p_device, devices.size(), ERR_INVALID_PARAMETER);
	String can_export_error;
	bool can_export_missing_templates;
	if (!can_export(p_preset, can_export_error, can_export_missing_templates)) {
		add_message(EXPORT_MESSAGE_ERROR, TTR("Run"), can_export_error);
		return ERR_UNCONFIGURED;
	}
	MutexLock lock(device_lock);
	EditorProgress ep("run", vformat(TTR("Running on %s"), devices[p_device].name), 3);
	String adb = get_adb_path();
	
	if (ep.step(TTR("Exporting APK..."), 0)) {
		return ERR_SKIP;
	}
	const bool use_wifi_for_remote_debug = EDITOR_GET("export/android/use_wifi_for_remote_debug");
	const bool use_remote = (p_debug_flags & DEBUG_FLAG_REMOTE_DEBUG) || (p_debug_flags & DEBUG_FLAG_DUMB_CLIENT);
	const bool use_reverse = devices[p_device].api_level >= 21 && !use_wifi_for_remote_debug;
	if (use_reverse) {
		p_debug_flags |= DEBUG_FLAG_REMOTE_DEBUG_LOCALHOST;
	}
	String tmp_export_path = EditorPaths::get_singleton()->get_cache_dir().path_join("tmpexport." + uitos(OS::get_singleton()->get_unix_time()) + ".apk");
#define CLEANUP_AND_RETURN(m_err)                         \
	{                                                     \