### 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)

r_features->push_back("etc2");
	r_features->push_back("astc");
	Vector<ABI> abis = get_enabled_abis(p_preset);
	for (int i = 0; i < abis.size(); ++i) {
		r_features->push_back(abis[i].arch);
	}
}
String EditorExportPlatformAndroid::get_export_option_warning(const EditorExportPreset *p_preset, const StringName &p_name) const {
	if (p_preset) {
		if (p_name == ("apk_expansion/public_key")) {
			bool apk_expansion = p_preset->get("apk_expansion/enable");
			String apk_expansion_pkey = p_preset->get("apk_expansion/public_key");
			if (apk_expansion && apk_expansion_pkey.is_empty()) {
				return TTR("Invalid public key for APK expansion.");
			}
		} else if (p_name == "package/unique_name") {
			String pn = p_preset->get("package/unique_name");
			String pn_err;
			if (!is_package_name_valid(pn, &pn_err)) {
				return TTR("Invalid package name:") + " " + pn_err;
			}
		} else if (p_name == "gradle_build/use_gradle_build") {
			bool gradle_build_enabled = p_preset->get("gradle_build/use_gradle_build");
			String enabled_plugins_names = _get_plugins_names(Ref<EditorExportPreset>(p_preset));
			if (!enabled_plugins_names.is_empty() && !gradle_build_enabled) {
				return TTR("\"Use Gradle Build\" must be enabled to use the plugins.");
			}
		} else if (p_name == "xr_features/xr_mode") {