Erased Internal Drive & lost my OS too!

Hi,

With great difficulty I upgraded my OS from Mojave to Ventura on my 2017 iMac.I wanted to erase the contents of the hard rive though.As per instruction I went into recovery mode & erased the disk through disk utility.When I restarted there was a question mark on the screen with a link to apple website which seemed to be an old link that was broken actually.

So I went back to recovery mode to reinstall the OS & found that it only gave the option of reinstalling Mojave! I did have a latest backup on Time Machine with Ventura but the computer did not recognize it & went to an old backup of Mojave with my data on the drive.I had no choice but to use it to restore the Mac.Once it is restored if I try to bring it to the latest backup (with Ventura on it) will it restore the OS to Ventura?

Any help on this would be appreciated.Thanks