How do I update Safari?

This is Chase Bank's problem to fix. They need to stop using the outdated and privacy-intrusive "user agent" query. They are the only major financial institution still doing that. Unfortunately, that leaves you out in the cold until they realize the error of their ways and correct it.

The workaround for end users who are unable to update their Macs to a newer macOS version is to use a different browser.

Consider Brave:

https://brave.com/

Firefox is a distant second choice:

https://www.mozilla.org/en-US/firefox/new/

The bottom line is that there is nothing wrong with your Mac's version of Safari, but that bank is using an outdated and ill-conceived method of determining browser requirements. If you are so motivated direct their attention to the WWW publication User-Agent Client Hints (courtesy VikingOSX).

In-depth background discussion here: chase wants me to update safari to 16, should I do that? - Apple Community

Updates for Safari come through Software Update within System Settings (formerly System Preferences). If you don't see an update for Safari, you'll need to update macOS — this updates Safari too.