Is there a Safari 16 update?

Your bank is the only such institution using an ill-conceived, outdated, privacy-intrusive "user agent" query to determine browser requirements. 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

Back up your data, check the application compatibility table, click here, and if your iMac is a 2014 or newer model, then on the download link for a higher OS. Alternatively, use a different web browser for their site.

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