There may be another explanation for why you cannot install banking apps from the App Store. The App Store may be showing you descriptions for apps that are designed to run on the iPhone and iPad.
Macs with Apple Silicon processors can run iPhone and iPad apps, if the developers of those apps allow it. Usually the App Store will hide iPhone and iPad apps that are not compatible with Apple Silicon Macs – but if you search for those apps from somewhere else (say, from Google), you might get a link that will cause the Mac App Store to open up, and show you the page for the iPhone or iPad app in question, plus a message that it is not compatible with your device. If you click for further details, you see text like "For iPhone and iPad only."
I can confirm that this definitely happens on Apple Silicon Macs. It might also happen on Intel-based ones (like the one you were gifted); the main difference being that an Intel-based Mac would always be incompatible with iPhone and iPad apps.
It is fairly common for businesses to
- Provide dedicated apps for mobile devices (iOS and Android smartphones and tablets)
- Expect Mac and Windows users to do without a dedicated app – and to instead, log into a Web site.
If that is the case, maybe all you need to do is to log into your bank's Web site. Ventura still gets the latest versions of Safari – and is likely to be eligible to run current versions of Firefox for several more years.