### 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)

String rcedit_path = EDITOR_GET("export/windows/rcedit");
	if (rcedit_path != String() && !FileAccess::exists(rcedit_path)) {
		add_message(EXPORT_MESSAGE_WARNING, TTR("Resources Modification"), vformat(TTR("Could not find rcedit executable at \"%s\"."), rcedit_path));
		return ERR_FILE_NOT_FOUND;
	}
	if (rcedit_path == String()) {
		rcedit_path = "rcedit"; 
	}
#ifndef WINDOWS_ENABLED
	
	String wine_path = EDITOR_GET("export/windows/wine");
	if (!wine_path.is_empty() && !FileAccess::exists(wine_path)) {
		add_message(EXPORT_MESSAGE_WARNING, TTR("Resources Modification"), vformat(TTR("Could not find wine executable at \"%s\"."), wine_path));
		return ERR_FILE_NOT_FOUND;
	}
	if (wine_path.is_empty()) {
		wine_path = "wine"; 
	}
#endif
	String icon_path;
	if (p_preset->get("application/icon") != "") {
		icon_path = p_preset->get("application/icon");
	} else if (GLOBAL_GET("application/config/windows_native_icon") != "") {
		icon_path = GLOBAL_GET("application/config/windows_native_icon");
	} else {
		icon_path = GLOBAL_GET("application/config/icon");
	}