Time Machine not recognizing reformatted external drive

It appears from your screenshot that the drive is not available for use as a Time Machine backup, not that it is not recognized by the system. If this is the case reformat the drive to APFS/GUID and try again. Everything I read says that Time Machine drives must be formatted APFS/GUID on Tahoe.

I can't see it in finder

In the System Settings, search for “Accessories.” It should show the section with Allow Accessories to Connect. Set it to always ask and connect the drive. Allow it to connect when asked.

Note this only applies to Apple Silicon (M-series) laptops.

Is this problematic drive being used on macOS 26.1 the same two drives from your other question

How to back up an external hard drive to another

There have been discussions, elsewhere , that using an External Drive " re-formatted it to journaled " which is HFS Journaled will work

Though, in those same discussions it has been mentioned TM Backup is Expecting the Destination Drive be formatted APFD / GUID Partition Map

The Error Message in your image seems to bear this out " Connect a suitable external drive "

Does the drive show up in Finder?

Apple Silicon laptops can prevent devices from connecting.

hootboot wrote:

Time machine doesn't recognise external drive, I have re-formatted it to journaled but still no response, it works fine on my old 2015 Mac, see attachment of screen shot. Thanks.

https://discussions.apple.com/content/attachment/eb78a64e-f1ee-4b17-a65e-79e93212f7d8

[Edited by Moderator]

You did mention the drive was re-formatted Journaled

Was the re-formatting done on this computers ?

Does this drive show up in Disk Utilities - Now ?