### 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 ext_filter = (get_os_name() == "Windows") ? "*.exe" : "";
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "custom_template/debug", PROPERTY_HINT_GLOBAL_FILE, ext_filter), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::STRING, "custom_template/release", PROPERTY_HINT_GLOBAL_FILE, ext_filter), ""));
	r_options->push_back(ExportOption(PropertyInfo(Variant::INT, "debug/export_console_wrapper", PROPERTY_HINT_ENUM, "No,Debug Only,Debug and Release"), 1));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "binary_format/embed_pck"), false));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "texture_format/bptc"), true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "texture_format/s3tc"), true));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "texture_format/etc"), false));
	r_options->push_back(ExportOption(PropertyInfo(Variant::BOOL, "texture_format/etc2"), false));
}
String EditorExportPlatformPC::get_name() const {
	return name;
}
String EditorExportPlatformPC::get_os_name() const {
	return os_name;
}
Ref<Texture2D> EditorExportPlatformPC::get_logo() const {