Hi crik91,
it really depends which additional software you use. Most data, generated by software that was installed via DietPi-Software, is stored in /mnt/dietpi_userdata/, so transfer at least this folder.
But some settings e.g. are also stored within e.g. /etc/. Pick and migrate the folders there, where you know the software and that you made settings adjustments to it.
But there are also other typical settings/data folder, e.g. /var/lib/ or /opt/, where special settings/data might be stored. It really depends, which software you use and if you really want to restore the exact behaviour of it.
In case of ownCloud and Nextcloud I made some backup script: https://dietpi.com/forum/t/owncloud-nextcloud-migration-script-for-v6-0-update/1867/1
Following the steps, will restore all data+settings safely on the new system.
I hope this helps a bid. In case name, which software you are thinking of explicitly.