Downgrading from MacOS Sonoma to Ventura

Over the weekend, my 2020 MacBook Air updated to macOS Sonoma without my prompting. I think it’s because I had the automatic updates option toggled but I digress. I am currently overseas and I am in need of Ventura to run a specific software that is currently not compatible with Sonoma.

I have tried everything as per Apple and google to downgrade. i tried to reinstall from internet recovery using both Shift-command-option-R and option-command-R.

when trying to reinstall using the shift-command-option-R it was giving me the option to download OS Catalina, but that was unsuccessful as I was getting an error message.

i then tried to create a bootable installer and install in recovery mode. All was good until i tried to select my Macintosh HD drive and was getting two separate errors. 1. “The volume cannot be downgraded.” And 2. “The operation couldn't be completed. (com.apple.BuildInfo.preflight.error error 21.)”

i have been in contact with Apple on and off for the past 2 days with no success.

reminder: I am overseas, and cannot just go to an Apple Store.

please help.