### 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)

ERR_FAIL_COND_V_MSG(filesystem_da.is_null(), ERR_CANT_CREATE, "Cannot create DirAccess for path '" + EditorPaths::get_singleton()->get_cache_dir() + "'.");
	filesystem_da->make_dir_recursive(EditorPaths::get_singleton()->get_cache_dir().path_join(id));
	String tmp_export_path = EditorPaths::get_singleton()->get_cache_dir().path_join(id).path_join("export.ipa");
#define CLEANUP_AND_RETURN(m_err)                                                                           \
	{                                                                                                       \
		if (filesystem_da->change_dir(EditorPaths::get_singleton()->get_cache_dir().path_join(id)) == OK) { \
			filesystem_da->erase_contents_recursive();                                                      \
			filesystem_da->change_dir("..");                                                                \
			filesystem_da->remove(id);                                                                      \
		}                                                                                                   \
		return m_err;                                                                                       \
	}                                                                                                       \
	((void)0)
	Device dev = devices[p_device];
	
	Error err = _export_project_helper(p_preset, true, tmp_export_path, p_debug_flags, dev.simulator, true);
	if (err != OK) {
		CLEANUP_AND_RETURN(err);
	}
	Vector<String> cmd_args_list;
	String host = EDITOR_GET("network/debug/remote_host");
	int remote_port = (int)EDITOR_GET("network/debug/remote_port");
	if (p_debug_flags & DEBUG_FLAG_REMOTE_DEBUG_LOCALHOST) {
		host = "localhost";
	}
	if (p_debug_flags & DEBUG_FLAG_DUMB_CLIENT) {
		int port = EDITOR_GET("filesystem/file_server/port");
		String passwd = EDITOR_GET("filesystem/file_server/password");
		cmd_args_list.push_back("--remote-fs");
		cmd_args_list.push_back(host + ":" + itos(port));