### 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)

_get_android_orientation_value(DisplayServer::ScreenOrientation(int(GLOBAL_GET("display/window/handheld/orientation"))));
	bool screen_support_small = p_preset->get("screen/support_small");
	bool screen_support_normal = p_preset->get("screen/support_normal");
	bool screen_support_large = p_preset->get("screen/support_large");
	bool screen_support_xlarge = p_preset->get("screen/support_xlarge");
	bool backup_allowed = p_preset->get("user_data_backup/allow");
	int app_category = p_preset->get("package/app_category");
	bool retain_data_on_uninstall = p_preset->get("package/retain_data_on_uninstall");
	bool exclude_from_recents = p_preset->get("package/exclude_from_recents");
	bool is_resizeable = bool(GLOBAL_GET("display/window/size/resizable"));
	Vector<String> perms;
	
	_get_permissions(p_preset, p_give_internet, perms);
	bool has_read_write_storage_permission = _has_read_write_storage_permission(perms);
	while (ofs < (uint32_t)p_manifest.size()) {
		uint32_t chunk = decode_uint32(&p_manifest[ofs]);
		uint32_t size = decode_uint32(&p_manifest[ofs + 4]);
		switch (chunk) {
			case CHUNK_STRINGS: {
				int iofs = ofs + 8;
				string_count = decode_uint32(&p_manifest[iofs]);
				string_flags = decode_uint32(&p_manifest[iofs + 8]);
				string_data_offset = decode_uint32(&p_manifest[iofs + 12]);
				uint32_t st_offset = iofs + 20;
				string_table.resize(string_count);
				uint32_t string_end = 0;
				string_table_begins = st_offset;
				for (uint32_t i = 0; i < string_count; i++) {
					uint32_t string_at = decode_uint32(&p_manifest[st_offset + i * 4]);
					string_at += st_offset + string_count * 4;