can I have Time Machine use my iCloud storage drive for my back ups?

I have a G-Drive ArmorATD disk, purchased from my local Apple store, connected to my MacBook Pro (Monterrey 12.5.1). It has stopped showing up as a connected drive, even after I really really carefully 'eject' it before shutting down my laptop for its nightly 'let's just start again' rest period. This is the third drive over which I have lost control and want to 'stop the insanity'. I would like to tell Time Machine to store my back-up info in my iCloud storage space (I have even purchased a bit more space to accommodate this). But I can't find out how to do it. Any guidance? Or is this impossible?

Also, can my iCloud storage space, which I think is supposed to jointly serve all the things I have attached to my Apple ID, use this space for their back-up stuff?