### 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)

String rk = p_preset->get_or_env("keystore/release", ENV_ANDROID_KEYSTORE_RELEASE_PATH);
	String rk_user = p_preset->get_or_env("keystore/release_user", ENV_ANDROID_KEYSTORE_RELEASE_USER);
	String rk_password = p_preset->get_or_env("keystore/release_password", ENV_ANDROID_KEYSTORE_RELEASE_PASS);
	if ((rk.is_empty() || rk_user.is_empty() || rk_password.is_empty()) && (!rk.is_empty() || !rk_user.is_empty() || !rk_password.is_empty())) {
		valid = false;
		err += TTR("Either Release Keystore, Release User AND Release Password settings must be configured OR none of them.") + "\n";
	}
	if (!p_debug && !rk.is_empty() && !FileAccess::exists(rk)) {
		valid = false;
		err += TTR("Release keystore incorrectly configured in the export preset.") + "\n";
	}
	String sdk_path = EDITOR_GET("export/android/android_sdk_path");
	if (sdk_path.is_empty()) {
		err += TTR("A valid Android SDK path is required in Editor Settings.") + "\n";
		valid = false;
	} else {
		Error errn;
		
		Ref<DirAccess> da = DirAccess::open(sdk_path.path_join("platform-tools"), &errn);
		if (errn != OK) {
			err += TTR("Invalid Android SDK path in Editor Settings.");
			err += TTR("Missing 'platform-tools' directory!");
			err += "\n";
			valid = false;
		}
		
		String adb_path = get_adb_path();
		if (!FileAccess::exists(adb_path)) {
			err += TTR("Unable to find Android SDK platform-tools' adb command.");
			err += TTR("Please check in the Android SDK directory specified in Editor Settings.");