### 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 name = dependency.get_file();
			if (added_embedded_dependenciy_names.has(name)) {
				continue;
			}
			added_embedded_dependenciy_names.push_back(name);
			plugin_embedded_dependencies.push_back(dependency);
		}
		plugin_files.append_array(plugin.files_to_copy);
		
		
		for (int j = 0; j < plugin.capabilities.size(); j++) {
			String capability = plugin.capabilities[j];
			if (p_config_data.capabilities.has(capability)) {
				continue;
			}
			p_config_data.capabilities.push_back(capability);
		}
		
		
		for (int j = 0; j < plugin.linker_flags.size(); j++) {
			String linker_flag = plugin.linker_flags[j];
			plugin_linker_flags.insert(linker_flag);
		}
		
		
		for (const KeyValue<String, PluginConfigIOS::PlistItem> &E : plugin.plist) {
			String key = E.key;
			const PluginConfigIOS::PlistItem &item = E.value;
			String value;
			switch (item.type) {