I'll add additional information here for someone who comes across this and is still trying to figure out how to add certain banking websites as a PWA.
I figured this out with my bank.
If you start a new tab with your search engine, enable desktop mode, then search your bank, you can follow the links to the online banking portion of their website. When you log into the desktop version of the online banking, try at that time to "Add to Home screen", name the shortcut, and try to open that link that was saved to your home screen. This works for my bank specifically, allows the webpage to open in a frameless app-style page, with the back buttons actually navigating the pages instead of closing it, like it did for me before with adding the mobile version of my banks online banking to my home screen.
Hope this helps someone.