### 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 (!p_force_save && customize_resources_plugins.is_empty() && customize_scenes_plugins.is_empty()) {
		return p_path; 
	}
	
	if (export_cache.has(p_path)) {
		FileExportCache &fec = export_cache[p_path];
		if (fec.saved_path.is_empty() || FileAccess::exists(fec.saved_path)) {
			
			uint64_t mod_time = FileAccess::get_modified_time(p_path);
			if (fec.source_modified_time == mod_time) {
				
				fec.used = true;
				return fec.saved_path.is_empty() ? p_path : fec.saved_path;
			}
			String md5 = FileAccess::get_md5(p_path);
			if (FileAccess::exists(p_path + ".import")) {
				
				md5 += FileAccess::get_md5(p_path + ".import");
			}
			if (fec.source_md5 == md5) {
				
				fec.source_modified_time = mod_time;
				fec.used = true;
				return fec.saved_path.is_empty() ? p_path : fec.saved_path;
			}
		}
	}
	FileExportCache fec;
	fec.used = true;
	fec.source_modified_time = FileAccess::get_modified_time(p_path);