As a long time Graphene OS user, I can tell you they don't. Almost no banks or credit card companies have a decent website even, let alone one that can replace thier apps.
So far I've yet to encounter any that have passkeys that could speed up the login process, and by using the website you've now fallen back to thier most involved login. You will have to login, then usually answer some security questions or complete a capture, then get the SMS code they sent you. Every time. For async notifications, some banks support emailing or texting you, but it tends to be poor. Hopefully you don't have one of the credit cards like Citi or Amex, which require you to verify flagged purchases via thier app. Otherwise it's a 10+ minute process to do it via phone call, and you have to guess that's why the transaction didn't go thru, call them yourself, get it approved, and try again. Instead of just clicking "yes, that's me" in the app when they prompt you about fraud. And if you click it fast enough, the original transaction might not even get rejected.
So no, the banking websites are not at all good substitute. And it's especially bad for certain banks.