You can use EUrail. It is very rare that further ID is asked for, and if there is an issue, its most often if one travels in the country of your passport. In such a case you should be able to prove you have now permanent citizenship in NZ. Though people like you are more likely to mostly use trains in that country for visiting F&R (friends and relatives). The official rules somewhere state you should have lived in an othercountry for at least 6 monthes with proof-in such a case a normal tourist entry will not be enough. It mostly also concerns f.e. British who travel extensively in UK-as local fares there are so sky high

No they don't @mcadv, as you've been told multiple times. You just need to be able to prove where you live.

Thanks both! I’ll go with Eurail and make sure I’m carrying proof of residency + visa with me (just in case).