Time Machine doesn't recognize my hard disk after initializing with OS journey extension

I have a MacBook Pro M1 from 2021 and I’m trying to do the back up so I took one of my hard disk and I try to delete the previous break up. There were still in progress, but system didn’t let me to move to the bin so I initialized the hard disk with the extension OS journey, but now when I select the option in time machine, it doesn’t show me this are disk. How can I solve the problem?

[Re-Titled by Moderator]