I did what you said up until the disks showed up. It was a HD disk and a Recovery disk. I tried the HD disk first to no avail. So I started over and when the disks showed up, I picked the Recovery disk. No external disks were offered.
Then a window showed up after picking English and hitting return as it instructed with four options:
1. Choice to restore TM backup. I don't use TM 2.Reinstall OS X - I don't have disks. They weren't provided 3. Get Help online - Duh! 4. Disk Utility - which is what I am supposing I am supposed to pick?
MacBook Pro - M2, Ventura 13.6 Safari Tech Prev 17.0 Safari 16.6 Firefox 116.0.2 iPhone 7 Version 15.8