I updated my Note 10 pro to 13.0.12.0 successfully using TWRP. I downloaded the update, copied to the sd card, rebooted in recovery mode, installed the update zip file, and rebooted.
I used the latest TWRP from nebrassy, TWRP-3.6.2, from 2022-07-25.
https://www.pling.com/p/1835160/