I'm not going to get into a discussion about this but instead present some alternate facts so that someday, if someone googles TLS and happens to find this page, they will have some food for thought.
The statement "TLS is not used by the banks per se, it is used by the browser to negotiate a connection to the bank" is simply untrue. You should try expanding your internet research and include the term "OpenSSL". We use this Open Source library to provide TLS 1.2 encryption services so a number of our outward-facing applications. And not just to browsers but also to the wire services for inter-bank transfers (high-value transactions).
"It is also a newer option that has only been the default connection method in the past few years "if" you are fully up to date" I don't know of any financial institutions that are not supporting TLS 1.2 (still effective even though it is now obsoleted by 1.3) as the default protocol. Our software is set to not downgrade to TLS 1.1 and I am pretty sure we are not the only geniuses that figured out the liability of automatically degrading our customer's security by falling back to a dangerous protocol without telling them. I urge people to click on the green padlock in the address bar of their favorite browser, then click Details, and confirm they are connected using TLS 1.2 and AES 256.
I think the issue is that you have a PC-centrist view of banking and not a good comprehension of how the back ends work. A browser is nothing more than an example of an application program that uses Internet protocols, lots of other applications use the same tools but are not browsers.
Regarding the topic of a VPN, I use one for work every day so I don't have to ever be in an office somewhere and I believe they have their place. If using a VPN makes one feel comfortable that's fine - as long as you remember that the VPN provider is the one collecting all of the information about your travels around the web, instead of whoever provided you access to the Internet. Since I have complete faith in the security protocols we use in our banking software and those same protocols are employed by the browser on my PC, I don't worry about using a VPN and, quite frankly, I don't care who knows where I've been on the web. It's a choice.
Dave
