Yes, look up Waydroid. But a lot of the banking apps and so on are explicitly designed to detect unusual running environments and thus will still not work. Android games etc. typically work fine though.
Linux Phones
Community about running GNU/Linux on phones. Projects like Ubuntu Touch, Plasma Mobile, PostmarketOS, Mobian etc. Either on former Android phones or hardware like the PinePhone.
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You aren't going to get banking apps to work easily. They are determined to ensure that your device is "trusted". They don't care about whether you trust it or not. These days a lot of them are using SafetyNet to ensure that the device is controlled by a known OEM. Software-based SafetyNet can be spoofed, but many devices now have Hardware-based SafetyNet which is incredibly difficult (as in there is not a known solution for most devices) to spoof. So if your bank is that annoying then you won't be able to use the app on any device that isn't running OEM firmware.
Personally I just use a web browser for my bank. If they are going to try and assert that the device is controlled by someone else than I don't want to know what other tricks they are trying. The sandbox of a web browser is where they belong IMHO.
I normally use web browser too, but bank imposes 2 factor authentication via their app for sign ins.
To add to this, you can also run Waydroid on Linux desktop. Could be a easier way to see of certain apps work.
I've used Waydroid on several Linux mobile OS and Waydroid is amazing. Literally no lag while running the apps, even old a low performance phone like the Pinephone.
Let me know of any issues you may have OP. Glad to help out