### 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)

uint16_t bpp = f->get_16(); 
			uint32_t img_size = f->get_32(); 
			uint32_t img_offset = f->get_32(); 
			if (w != h) {
				continue;
			}
			
			uint64_t prev_offset = f->get_position();
			images[w].pal_colors = pal_colors;
			images[w].planes = planes;
			images[w].bpp = bpp;
			images[w].data.resize(img_size);
			f->seek(img_offset);
			f->get_buffer(images[w].data.ptrw(), img_size);
			f->seek(prev_offset);
		}
	} else {
		Ref<Image> src_image;
		src_image.instantiate();
		err = ImageLoader::load_image(p_src_path, src_image);
		ERR_FAIL_COND_V(err != OK || src_image->is_empty(), ERR_CANT_OPEN);
		for (size_t i = 0; i < sizeof(icon_size) / sizeof(icon_size[0]); ++i) {
			int size = (icon_size[i] == 0) ? 256 : icon_size[i];
			Ref<Image> res_image = src_image->duplicate();
			ERR_FAIL_COND_V(res_image.is_null() || res_image->is_empty(), ERR_CANT_OPEN);
			res_image->resize(size, size, (Image::Interpolation)(p_preset->get("application/icon_interpolation").operator int()));
			images[icon_size[i]].data = res_image->save_png_to_buffer();
		}
	}
	uint16_t valid_icon_count = 0;