### 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)

EditorExportPlatformAndroid *ea = static_cast<EditorExportPlatformAndroid *>(ud);
	while (!ea->quit_request.is_set()) {
#ifndef DISABLE_DEPRECATED
		
		{
			
			if (!ea->android_plugins_changed.is_set()) {
				Vector<PluginConfigAndroid> loaded_plugins = get_plugins();
				MutexLock lock(ea->android_plugins_lock);
				if (ea->android_plugins.size() != loaded_plugins.size()) {
					ea->android_plugins_changed.set();
				} else {
					for (int i = 0; i < ea->android_plugins.size(); i++) {
						if (ea->android_plugins[i].name != loaded_plugins[i].name) {
							ea->android_plugins_changed.set();
							break;
						}
					}
				}
				if (ea->android_plugins_changed.is_set()) {
					ea->android_plugins = loaded_plugins;
				}
			}
		}
#endif