In most projects this part is unnecessary because you only need the capabilities from Tokio that Tauri re-exports in tauri::async_runtime. However, if you need more advanced functionalities from the broader Tokio ecosystem there’s absolutely nothing wrong with adding it directly.
In order to spawn a background thread in Tauri all you have to do is use tauri::async_runtime::spawn(). This will schedule an async function to be executed by one of the Tokio runtimes worker threads.