Banana

You'll likely be seen as a "non-traditional" candidate to be honest - while in reality the "penultimate student" rule isn't mandatory, it does make your profile a trickier one for an HR team processing thousands of applications (in some banks now, using data tools which screen for that kind of thing), at least for internships. It'll be hard, but not impossible, so you should still try.

I think you should cast your net wide, however. BB banks will be very difficult for anyone, so don't expect a high likelihood of hearing back. I'd consider boutique shops, big 4 audit (and transaction services roles), and perhaps in-house corporate roles.

I don't know what your financial situation is like, but you want to avoid being out of work at least from a career perspective, as the gap in your CV will look increasingly challenging to explain.

Finally, and I know it goes without saying, but try to work on a "story". Travelling a lot and being "too late" won't be taken well as explanations for why you didn't apply sooner.

Best of luck!