I’d like to be able to use it along with my wife, ideally painlessly. Is that going to be possible?
That depends upon how painless it is to deal with your wife.
I asked the same question in the comments section some months ago and was told by Anova that it pairs with one device at a time.
Kinda like my Bluetooth speaker thing that I have at home. If one of my kid’s devices is still paired with it then i can’t.
This is a limitation of all Bluetooth devices. They can only be controlled by one phone, computer, etc. at a time. However, if you own multiple cookers it would be possible to control all of them from the same phone, computer, etc.