I do banking on it and I have been getting notices that my operating system is not up to date and recommended to update to a new version that is supported.
I hate those knee-jerk notices. If you're using a good, reasonably current browser and have a https connection, the underlying OS isn't really going to make any difference. You're actual vulnerability is if the OS -- regardless of whether it's 10, 11 or 7 -- becomes compromised from visiting bad sites, and that can carry over to affect your interaction with more sensitive sites. So the ultimate resolution you choose will depend on what type of internet user you are.
I have no qualms about using Win 7 for my banking. I do not consider it to be any less secure than Win 10/11. Any vulnerabilities that aren't being patched are mostly esoteric, IMHO. (In fact, I trust my Win 7 machine more than my wife's Win 10 machine.) I don't do social media and only use a VM to visit sketchy sites, so any scenario where 7 might be more vulnerable than 10 is a scenario I don't ever expect to find myself in anyway.
The best way, however, would be to setup a VM to isolate your sensitive activities (your banking) from general activities (social media and visiting unfamiliar or sketchy sites). Even a Win 7 VM can be used safely if you're running a sandboxed OS that isn't coming in contact with sketchy sites.
So setup a VM dedicated solely to doing your banking, or alternatively setup a VM dedicated to general internet surfing. Either way is fine as long as the OS under which you're doing your banking is not the one you're exposing to general internet surfing.
If Mint is too slow in a VM, you should be able to find an alternate linux that is less demanding and lighter on system resources. If that's still too much trouble, consider buying an inexpensive Chromebook and using that instead.
As for your immediate problem of banks telling you to upgrade your OS, just use a User Agent Switcher extension. There are plenty of extensions for all the major browsers, and what they do is mask your internet connection to the bank and pretend to be a different browser, browser version, and/or OS. The bank won't know you're using Win 7 if the User Agent Switcher tells the bank you're using Win 10.