I found the solution for installing custom ROMs for the first time and it's a far cry from the process described on the first page. It always involves losing your data. I am in doubt that there's a good process at the moment that'll allow you to keep your data when moving away from the stock ROM. In short, the process involves this:
1. Put the phone into
fastboot mode. Do not install TWRP but simply boot into it with i.e.
2. When in TWRP
transfer your ROM (and Magisk if you want root) from your PC to the internal storage. With the correct drivers on your PC you should be able to do a data transfer as always.
Flash ROM and optionally Magisk. Do not flash DMVerity remover!
3. After you have successfully flashed ROM and Magisk, reboot once again into
recovery, not into system.
4. You'll now find yourself in stock recovery. You'll have to do a
data wipe. After that you can boot into the system of your new ROM. That's it.
You might be able to flash TWRP permanently after this but I would advise against it. Incompatible TWRP is the main source of bootloops (fastboot and recovery loops amongst them). For some reason stock recovery is the only way to correctly wipe the data partition. This might have something to do with the filesystem and/or SE Linux context but until somebody finds out a secure alternative method I for my part will not flash TWRP.
If you want to upgrade your custom ROM the next time, you should be able to do it with steps 1-3, booting into system after that.