### 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)

switch (p_filter) {
		case EditorExportPreset::EXCLUDE_SELECTED_RESOURCES:
			return TTR("Resources to exclude:");
		case EditorExportPreset::EXPORT_CUSTOMIZED:
			return TTR("Resources to override export behavior:");
		default:
			return TTR("Resources to export:");
	}
}
void ProjectExportDialog::_filter_changed(const String &p_filter) {
	if (updating) {
		return;
	}
	Ref<EditorExportPreset> current = get_current_preset();
	if (current.is_null()) {
		return;
	}
	current->set_include_filter(include_filters->get_text());
	current->set_exclude_filter(exclude_filters->get_text());
}
void ProjectExportDialog::_fill_resource_tree() {