To best gauge AeT using nose breathing, you want to make sure you precede the test with a very thorough, very gradual warm up. If you jump into it too soon, you’ll be able to still breathe through your nose, but lactate levels will be above your aerobic threshold.
I don’t know why this is, but I’ve tested it with my lactate meter. If I ramp up too much too soon, I can still breathe through my nose with lactate around ~3. To avoid that, I would warm up very slowly for at least a half hour.
This is important to get right. Training above your AeT without knowing it will create unwanted adaptations. Training below your AeT without knowing it has no disadvantages.
I suspect your AnT is reasonably close given your description of the effort.