how to I update my safari browser , I'm having trouble, I have 15. need 16

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 as needed.

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Chase Bank is the only such institution using an outdated, ill-conceived and privacy-intrusive "browser check". Why they are doing that is anyone's guess, but it's irresponsible and serves no beneficial purpose.

If you are so motivated direct Chase Bank's attention to the WWW publication User-Agent Client Hints (courtesy VikingOSX from this Discussion if you want to read more).

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:

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

The bottom line is that there is nothing wrong with your Mac's version of Safari. It is every bit as secure as later versions. Chase ought to stick to banking, or whatever it is they do.

Am I correct in assuming the trouble you are experiencing is the Chase Bank website?

👍

Your computer is just fine.