With banking apps, most rely on SMS texts for verification, so by default that means the code must come to a cellular telephone. If you're using the Bank's App on that same phone, then yes, you get in using just the one device. That's how my Bank of America app works, and in fact, since I'm using messages in iCloud, that SMS verification code does indeed come to all my Apple devices at the same time. So I am always logging in and receive my two step login code on the exact same device whenever I access my back account, retirement account, investment account, etc.
Apple uses iCloud notifications to push the code out to all your trusted devices, linked by the common AppleID used on them all. They had to do that so that devices other than iPhones would work with 2FA (although you can also enroll a SMS capable cellular telephone number as a backup for codes or a landline for voice codes). My backup number for 2FA codes is a Google voice number, so not a device at all, just a SMS capable VOIP service.