However, my bank requires second factor for authenticating, when using the banking website. And that second factor used to be SMS, but nowadays it is their bank

However, my bank requires second factor for authenticating, when using the banking website. And that second factor used to be SMS, but nowadays it is their banking app on a mobile device. Exactly that one that has to run on "genuine, unmodded, unrooted version of the hardware and OS it came with".