External hard “Mac OS Extended” & Disk “APFS”

I use Time Machine to make a backup of my Mac using a external hard which its format “Mac OS Extended”,

then Option-⌘-R to go macOS recovery for upgrade to the latest macOS that is compatible with my Mac,

after that I decided to erase (format) my disk selecting Disk Utility to erase the disk and making the Format “APFS” ,

finally Install macOS

Now, I want to restore my Mac from a backup which on external hard “Mac OS Extended”

The problem is, I didn’t see the external hard ;

I think the issue is , the disk is “APFS” format and the external hard is “Mac OS Extended”

what I should do? and if I convert it to APFS will the external hard shown without earsing the hard?

I try to copy and past the file on the time machine and I get this error “the volume has the wrong case sensitivity”