Shortcut: Buy HAT-402 (~60€), replace whichever HT-802 you use (~30 minutes), follow Nuki App instructions, save you the pain of trying to force fit a system that is just not compatible.
I reached out to Elcom / Hager and the customer support confirmed that HAT-402 replaces all HT-802 systems; HT Uni 2 replaces all 402 and 302 systems. I tried the HAT-402. It is very simple to upgrade the system, the default wiring remains unchanged. However, it might be necessary to replace the out station speaker (ELA-402) if it was produced in 2006 or earlier.
It is okay if you just replace one HT-802 with a HAT-402. You do not need to change all stations. As far as I can tell, it just works fine without interferences.