I'm happy that my bank (still) allows me to have both a stand-alone reader and a mobile app to authenticate. Because if you lose your authentication device, a lot of things suddenly get a lot harder.

I also tried to use an old phone as a backup device. However, most authentication apps only allow it to be installed on a single device.

I did that too (in Austria) for a long time. Fortunately my Bank (Erste Bank / Sparkasse) fully (almost fully, no nfc pay, since it depends on GPay) supports GrapheneOS now