### 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)

f->store_line("NSDownloadsFolderUsageDescription = \"" + downloads_folder_usage_descriptions[lang].operator String() + "\";");
			
			if (network_volumes_usage_descriptions.has(lang)) {
				f->store_line("NSNetworkVolumesUsageDescription = \"" + network_volumes_usage_descriptions[lang].operator String() + "\";");
			
			if (removable_volumes_usage_descriptions.has(lang)) {
				f->store_line("NSRemovableVolumesUsageDescription = \"" + removable_volumes_usage_descriptions[lang].operator String() + "\";");
			
			if (copyrights.has(lang)) {
				f->store_line("NSHumanReadableCopyright = \"" + copyrights[lang].operator String() + "\";");
			
		
	
	// Now process our template.
	bool d_binary = false;
	int export_angle = p_preset->get("application/export_angle");
	bool include_angle_libs = false;
	if (export_angle == 0) {
		include_angle_libs = String(GLOBAL_GET("rendering/gl_compatibility/driver.macos")) == "opengl3_angle";
	 else if (export_angle == 1) {
		include_angle_libs = true;
	
	while (ret == UNZ_OK && err == OK) {
		// Get filename.
		unz_file_info info;
		char fname[16384];
		ret = unzGetCurrentFileInfo(src_pkg_zip, &info, fname, 16384, nullptr, 0, nullptr, 0);
		if (ret != UNZ_OK) {
			break;