For a recent multi stop booking ticketed by NZ which has a domestic UA segment, I went to the UA website plugged in the UA booking reference and upgraded the UA domestic flight to First. I have done this several times over the last few years without any hiccups until now.

I refreshed my NZ app the next day and the UA flight on the itinerary was still showing Economy, plus the seat and meal selection on all the NZ flights had disappeared and other things you see under each flight segment simply said 'Refer to ticket'.
When I clicked Manage booking on the app, it threw an error and I had the same issue on the desktop site as well.
I called NZ last night and the first agent I spoke to said he couldn't access the booking 'completely' and said it was a travel agent booking and then told me to call United to sort it out after I told him what I had done with the UA flight.
I knew United couldn't do anything as it is NZ ticket stock so called NZ again this morning, she consulted with a supervisor and said the reason it was indeed due to the UA upgrade which they didn't know about (UA is responsible for letting NZ know about the upgraded segment) and she was surprised I could upgrade the domestic UA flight directly on UA's website.
The second thing she said was due to the processing of APD upgrade on one of the NZ flights in the itinerary (which I had posted about here) - when the upgrade didn't clear straight away on NZ1, I had called them in the weekend to enquire and the agent recommended changing to NZ5 that day as she could see R class availability. So she had made the changes but had to send it off to a special team to process and confirm it but she hadn't released my PE seat on the original flight I was booked on and that was another potential reason it corrupted the whole booking.

Anyways, it was all sorted out in the end by a very helpful agent this morning and all the flight segments are now showing correctly and Manage Booking link is working as it should. Think I might just leave the UA segment alone in future or wait a few days before upgrading.