My mac is currently running on macOS Big Sur Version 11.7.10 which I think is the most current. However,my safari is version 16.6.1 which is not the up to date version. How can I update my safari? I do the upgrades on system preferences regularly.

Safari is only updated with the OS. The reason for this is that Safari uses the WebKit components of the OS that is installed on the Mac. If you are unable to update the OS, then Safari will not be able to be updated either.

In some cases you can use a different browser instead of Safari to access sites that require a newer version of Safari, but since you are having Microsoft not being able to update also, it may be time to upgrade your computer to a newer model. I know this is not what you want to hear, but you probably have a Mac that is 9 years or older and they just did not have the hardware available back then to support the security improvements in the newer OS versions that Safari now uses and apparently Microsoft is requiring for the update as well.