### 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)

static const uint8_t icon_size[] = { 16, 32, 48, 64, 128, 0  };
	struct IconData {
		Vector<uint8_t> data;
		uint8_t pal_colors = 0;
		uint16_t planes = 0;
		uint16_t bpp = 32;
	};
	HashMap<uint8_t, IconData> images;
	Error err;
	if (p_src_path.get_extension() == "ico") {
		Ref<FileAccess> f = FileAccess::open(p_src_path, FileAccess::READ, &err);
		if (err != OK) {
			return err;
		}
		
		f->get_16(); 
		uint16_t icon_type = f->get_16(); 
		uint16_t icon_count = f->get_16(); 
		ERR_FAIL_COND_V(icon_type != 1, ERR_CANT_OPEN);
		for (uint16_t i = 0; i < icon_count; i++) {
			
			uint16_t w = f->get_8(); 
			uint16_t h = f->get_8(); 
			uint8_t pal_colors = f->get_8(); 
			f->get_8(); 
			uint16_t planes = f->get_16();