### 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_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "gradle_build/min_sdk", PROPERTY_HINT_PLACEHOLDER_TEXT, vformat("%d (default)", VULKAN_MIN_SDK_VERSION)), "", false, true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "gradle_build/target_sdk", PROPERTY_HINT_PLACEHOLDER_TEXT, vformat("%d (default)", DEFAULT_TARGET_SDK_VERSION)), "", false, true));
#ifndef DISABLE_DEPRECATED
	Vector<PluginConfigAndroid> plugins_configs = get_plugins();
	for (int i = 0; i < plugins_configs.size(); i++) {
		print_verbose("Found Android plugin " + plugins_configs[i].name);
		r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, vformat("%s/%s", PNAME("plugins"), plugins_configs[i].name)), false));
	}
	android_plugins_changed.clear();
#endif 
	
	
	const Vector<ABI> abis = get_abis();
	for (int i = 0; i < abis.size(); ++i) {
		const String abi = abis[i].abi;
		
		
		const bool is_default = abi == "arm64-v8a";
		r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, vformat("%s/%s", PNAME("architectures"), abi)), is_default));
	}
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "keystore/debug", PROPERTY_HINT_GLOBAL_FILE, "*.keystore,*.jks", PROPERTY_USAGE_DEFAULT | PROPERTY_USAGE_SECRET), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "keystore/debug_user", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_DEFAULT | PROPERTY_USAGE_SECRET), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "keystore/debug_password", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_DEFAULT | PROPERTY_USAGE_SECRET), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "keystore/release", PROPERTY_HINT_GLOBAL_FILE, "*.keystore,*.jks", PROPERTY_USAGE_DEFAULT | PROPERTY_USAGE_SECRET), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "keystore/release_user", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_DEFAULT | PROPERTY_USAGE_SECRET), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "keystore/release_password", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_DEFAULT | PROPERTY_USAGE_SECRET), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::INT, "version/code", PROPERTY_HINT_RANGE, "1,4096,1,or_greater"), 1));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "version/name", PROPERTY_HINT_PLACEHOLDER_TEXT, "Leave empty to use project version"), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "package/unique_name", PROPERTY_HINT_PLACEHOLDER_TEXT, "ext.domain.name"), "com.example.$genname", false, true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "package/name", PROPERTY_HINT_PLACEHOLDER_TEXT, "Game Name [default if blank]"), ""));