I'm not sure if buying a phone for the sole (or primary) purpose of using internet banking is necessarily the best investment (given the OP's reluctance to use internet-based banking), and would be a double whammy of mastering new technology (a phone) as well as a new interface (internet-based banking) - so perhaps the first step could be simply setting it up to use via a web browser on a computer?

Kiwibank's web-based interface is fine - I hardly ever use it, as their phone app is good enough to complete all day-to-day banking tasks and is much easier to log in (using a fingerprint - but it does the job.

The worst thing is their 2FA is stuck in the previous decade, with a question and answer based approach; they have introduced text-based 2FA for some transactions, I noticed.

And, as far as age goes, I only recently removed internet banking from my mother's iPad - she's been using it ok up until a couple of years ago, and she'll turn 85 this year. Her dementia, though, doesn't help her - I manage her finances and found I was regularly locked out due to too many incorrect log-in attempts...