Safari 15.6.1 is the highest possible Safari version with Catalina.
Safari 16.6.1 is available with Big Sur and 17.3 with Monterey and later.
To upgrade Safari from Safari 15.6.1 to a later version you would need to upgrade your Mac from macOS 10.15.7 to a later version.
If you can’t or don’t want to upgrade, you may want to use a 3rd party internet browser that supports running their current version on your Mac. One option is Chrome: https://www.google.com/chrome/
The model year of a MacBook Pro is available at Apple menu > About This Mac.
An Early 2008 through mid 2009 MacBook Pro can be upgraded to El Capitan 10.11.6 but no later version.
A mid 2010 through late 2011 MacBook Pro can be upgraded to High Sierra 10.13.6 but no later version.
A mid 2012 through early 2013 MacBook Pro can be upgraded to Catalina 10.15.7 but no later.
A late 2013 and mid 2014 MacBook Pro can be upgraded to the latest version of Big Sur macOS 11 but no later.
An early 2015 through 2016 MacBook Pro can be upgraded to the latest version of Monterey macOS 12 but no later.
A 2017 MacBook Pro can be upgraded to the current version of Ventura macOS 13.
For all of the above, see instructions in: How to download and install macOS - Apple Support
A 2018 or later MacBook Pro can be upgraded to the current version of Sonoma macOS 14. See: How to upgrade to macOS Sonoma - Apple Support