How do I update Safari on my Mac? My bank is requiring the update to access their system.

Safari is part of the MacOS. Keep your Mac up to date and Safari will also be up to date. The most recent version of MacOS is 12.x.x

Learn the maximum MacOS for your system here https://everymac.com/systems/by_capability/maximum-macos-supported.html

Sometimes upgrading the OS and Safari works. Sometimes not. If that happens, then I suggest installing a second browser such as Firefox or Chrome. They will usually work fine.