OUTDATED: Look down below for proper solution as this will result in missing waiting tone whole calling somebody with VoLTE enbavled.
TL;DR: Reinstall with Android 13 fw and Android 11 binaries when reinstalling SFOS to get VoLTE working.
I just reinstalled my Xperia 10 iii with Android 13 62. 2 .A.0.533 using EMMA on Windows, then installing Sailfish 4.4.0.64 with Android 11 binaries (SW_binaries_for_Xperia_Android_11_4.19_v9a_lena.zip) as stated in the original Linux install instructions. Only thing I did differently was to run sudo ./flash.sh --extra-opts “-S 512K” to get around this error: " FAILED (remote: Requested download size is more than max allowed)"
To my surprise VoLTE worked after updating to 4.4.0.68, keeps working after upgrading to 4.4.0.72 (not a stop release) and 4.5.0.25 and 4.6.0.15. I can browse the internet over 4G while in a call and send and receive text messages at the same time. I have Hallo DK which is a on the Danish TDC mobile network.
There might be an easier way to do this and preserve SFOS installation with settings according to this: Android 13 and SailfishOS on Xperia 10 III - #121 by olf