Fresh installation of MacOS - Time Machine disk not recognized

I wanted to give my MacBook Air (2014) a new lease of life, as it has been quite sluggish for some time now. So I decided to erase the hard drive and start fresh with a new installation of the OS (in fact it was an upgrade to Mojave 10.14.6 - not sure if that's the most recent OS that this machine can handle?).

I did a Time Machine backup, but there was only one thing I wanted to bring over post-reset: my Photos library. I have a 2TB iCloud plan, and I use the Photos app on Mac to do sorting/keyword management.

For this reason, I did not do a full back up from Time Machine during the reset (while in Recovery mode). I wanted the fresh installation, and then just cherry pick the Photos library from my Time Machine.

However, when I plugged in my Time Machine disk (WD Passport), it was not recognized by the computer. It's being treated like a brand new disk, as though I was setting up Time Machine for the first time.

The backups are indeed on the disk, which I've confirmed through file browsing via finder. But I cannot enter Time Machine on the Mac in order to restore the Photos library.

Any help much appreciated.