### 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 valid = true;
#ifndef ANDROID_ENABLED
	String templates_error;
	valid = valid && has_valid_export_configuration(p_preset, templates_error, r_missing_templates, p_debug);
	if (!templates_error.is_empty()) {
		r_error += templates_error;
	}
	String export_plugins_warning;
	Vector<Ref<EditorExportPlugin>> export_plugins = EditorExport::get_singleton()->get_export_plugins();
	for (int i = 0; i < export_plugins.size(); i++) {
		Ref<EditorExportPlatform> export_platform = Ref<EditorExportPlatform>(this);
		if (!export_plugins[i]->supports_platform(export_platform)) {
			continue;
		}
		String plugin_warning = export_plugins.write[i]->_has_valid_export_configuration(export_platform, p_preset);
		if (!plugin_warning.is_empty()) {
			export_plugins_warning += plugin_warning;
		}
	}
	if (!export_plugins_warning.is_empty()) {
		r_error += export_plugins_warning;
	}
#endif