Lately a couple of sites I frequent have said they will no longer support my browser. I have Safari 12.1.2 on my laptop with macOS Sierra 10.12.6. When I look, it says there are no updates, so how do I update?

The model year of a MacBook Pro is available at Apple menu > About This Mac.

A mid-2010 through late-2011 MacBook Pro can be upgraded to High Sierra 10.13.6 but no later version. See: https://support.apple.com/en-us/HT211683

A mid-2012 through early-2013 MacBook Pro can be upgraded to Catalina 10.15.7. See: https://support.apple.com/en-us/HT211683

A late-2013 or later can be upgraded to the current version of Big Sur. See: https://support.apple.com/en-us/HT201475

I think I can explain what is happening. If you are unable to access certain web sites and getting a message that your browser must be updated, this is not an unusual situation. The reason is that web site engineers write their software to work with specific browsers and specific versions of them. You can hope that your web site's developers eventually update their site to work with Safari, or you can use another browser that does work such as Firefox or Chrome. They can be individually updated as needed. It is important to know that Safari is installed as part of the operating system and it normally it cannot be individually updated. Safari is periodically updated when the computer's operating system (OS) is updated or upgraded. Finally, even if you are able to update Safari, there is no guarantee that it will be compatible with every web site. This is why many of us have more than one browser installed.