I can't update Safari

Safari is updated when you upgrade the operating system on your MacBook Pro.

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: How to download macOS - Apple Support

A mid 2012 through early 2013 MacBook Pro can be upgraded to Catalina 10.15.7 but no later. See: How to download macOS - Apple Support

A late 2013 and mid 2014 can be upgraded to the latest  version of Big Sur macOS 11 but no later. See: How to download macOS - Apple Support

An early 2015 through 2016 MacBook Pro can be upgraded to the latest version of Monterey macOS 12. See: How to download macOS - Apple Support

A 2017 or later MacBook Pro can be upgraded to the current version of Ventura macOS 13. See: How to upgrade to macOS Ventura - Apple Support

Be aware that if you upgrade to Catalina 10.15 or later you will also need to update any non-Apple 32-bit apps. See: https://www.macworld.com/article/232735/how-to-check-if-mac-software-is-32-or-64-bit.html

If you can't or don't want to upgrade the operating system, consider, for security reasons, using a 3rd party browser that supports running their current version with your macOS 13. Possibilities include Chrome and Firefox.

If you are unable to upgrade macOS because your Mac is too old, your alternatives are to use another browser with the security features they need.

I recommend Brave:

https://brave.com/

If Brave is not an option for your Mac, Firefox is another possible choice:

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

I do not recommend Google for many reasons. Installing Google on a Mac too old for more recent macOS versions will cause it to run objectionably slow.