How to use async/await/loadAsync when loading a material texture image

In my example I’m using
await mtlLoader.loadAsync( mtlFilename ).then( onLoad_mtlLoader )
instead of MTLLoader.load()
Within onLoad_mtlLoader I call:
let objInstance = await objLoader.loadAsync(objFilename);
and then I call onLoad_FileObj_objLoader (which is not async, so no need to await for it)
onLoad_FileObj_objLoader(objInstance);

This is all done before calling renderer.render( scene, camera );

So I expect that by the time that the rendering is called, the texture is fully loaded. This can be seen in here.
Can you show where the code is not waiting?

Regarding LoadingManager, I’m using it but for a different purpose (for adjusting the url)
Can you give an example how to pass in the LoadingManager and how to use the LoadingManager.onLoad(), with async/await?

I could have continued call the rendering and the continue the rest of the program from within the callback onLoad_FileObj_objLoader, but I thought I can use async/await/loadAsync (for better clarity).

(btw: I learned about loadAsync() instead of load() in one of your comments from another question, and I thought async/awit/loadAsync() can work together to replace the callback-hell)

Thank you!