### 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)

if (ret != UNZ_OK) {
			break;
		}
		bool skip = false;
		String file = String::utf8(fname);
		Vector<uint8_t> data;
		data.resize(info.uncompressed_size);
		
		unzOpenCurrentFile(pkg);
		unzReadCurrentFile(pkg, data.ptrw(), data.size());
		unzCloseCurrentFile(pkg);
		
		if (file == "AndroidManifest.xml") {
			_fix_manifest(p_preset, data, p_give_internet);
		}
		if (file == "resources.arsc") {
			_fix_resources(p_preset, data);
		}
		
		if ((file == SPLASH_IMAGE_EXPORT_PATH || file == LEGACY_BUILD_SPLASH_IMAGE_EXPORT_PATH) && splash_image.is_valid() && !splash_image->is_empty()) {
			_load_image_data(splash_image, data);
		}
		
		if ((file == SPLASH_BG_COLOR_PATH || file == LEGACY_BUILD_SPLASH_BG_COLOR_PATH) && splash_bg_color_image.is_valid() && !splash_bg_color_image->is_empty()) {
			_load_image_data(splash_bg_color_image, data);
		}
		if (file.ends_with(".png") && file.contains("mipmap")) {
			for (int i = 0; i < icon_densities_count; ++i) {
				if (main_image.is_valid() && !main_image->is_empty()) {
					if (file == launcher_icons[i].export_path) {