Sideload 6T from Android 11 to Android 13 (T) using Zorin OS

Not certain what you are asking.

The “new feature” to Upgrade Android version without loss of data really only applies to Upgrades from S → T.

In any case, essentials should be backed up before any significant job.

I seem to remember some users reported an Upgrade R → S where data was not lost in the Upgrade, however at that stage users were asked to make a full backup.

A search of the forum might find those reports.

You are likely to be one of the first if you decide to try R → T

I have no first hand experience, but provided an answer to a similar issue Motorola - Moto G7 Play - channel - Documentation Suggestions - #3 by aibd. Notice that in the “upgrade to T” pages, there is the inclusion of sideloading recovery along with the regular system image.