### 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)

String path = E;
		String type = ResourceLoader::get_resource_type(path);
		if (FileAccess::exists(path + ".import")) {
			
			String export_path = _export_customize(path, customize_resources_plugins, customize_scenes_plugins, export_cache, export_base_path, false);
			if (export_path != path) {
				
				
				Ref<ConfigFile> config;
				config.instantiate();
				err = config->load(path + ".import");
				if (err != OK) {
					ERR_PRINT("Could not parse: '" + path + "', not exported.");
					continue;
				}
				config->set_value("remap", "type", ResourceLoader::get_resource_type(export_path));
				
				List<String> keys;
				config->get_section_keys("remap", &keys);
				for (const String &K : keys) {
					if (K.begins_with("path")) {
						config->erase_section_key("remap", K);
					}
				}
				
				config->set_value("remap", "path", export_path);
				
				config->erase_section("deps");
				config->erase_section("params");
				String import_text = config->encode_to_text();