### 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)

bool first_build = last_gradle_build_time == 0;
	bool have_plugins_changed = false;
	String plugin_names = _get_plugins_names(p_preset);
	if (!first_build) {
		have_plugins_changed = plugin_names != last_plugin_names;
#ifndef DISABLE_DEPRECATED
		if (!have_plugins_changed) {
			Vector<PluginConfigAndroid> enabled_plugins = get_enabled_plugins(p_preset);
			for (int i = 0; i < enabled_plugins.size(); i++) {
				if (enabled_plugins.get(i).last_updated > last_gradle_build_time) {
					have_plugins_changed = true;
					break;
				}
			}
		}
#endif 
	}
	last_gradle_build_time = OS::get_singleton()->get_unix_time();
	last_plugin_names = plugin_names;
	return have_plugins_changed || first_build;
}
Error EditorExportPlatformAndroid::export_project(const Ref<EditorExportPreset> &p_preset, bool p_debug, const String &p_path, int p_flags) {