### 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 can_export = EditorExport::get_singleton()->get_export_preset_count() > 0;
	for (int i = 0; i < EditorExport::get_singleton()->get_export_preset_count(); i++) {
		Ref<EditorExportPreset> preset = EditorExport::get_singleton()->get_export_preset(i);
		bool needs_templates;
		String error;
		if (preset->get_export_path().is_empty() || !preset->get_platform()->can_export(preset, error, needs_templates)) {
			can_export = false;
			break;
		}
	}
	export_all_button->set_disabled(!can_export);
	if (can_export) {
		export_all_button->set_tooltip_text(TTR("Export the project for all the presets defined."));
	} else {
		export_all_button->set_tooltip_text(TTR("All presets must have an export path defined for Export All to work."));
	}
}
void ProjectExportDialog::_edit_preset(int p_index) {