How do I update to Safari 15?

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

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. See: https://support.apple.com/en-us/HT211683

A mid 2010 through late 2011 MacBook Pro can be upgraded to High Sierra 10.13.6 but no later version. See: How to get old versions of 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 get old versions of 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 get old versions of macOS - Apple Support

An early 2015 or later can be upgraded to the current version of Monterey macOS 12. See: How to upgrade to macOS Monterey - Apple Support

While different than update Safari; another idea may be

to see if there are expired secure certificates for browser.

• Digital certificates and encrypted websites in Safari on Mac - Apple Support

If so, and certain sites you'd previously visited, w/o issue

may not view those certificates as valid now, after expiry.

• Certificate Transparency : Certificate Dev

https://certificate.transparency.dev/

About Let's Encrypt - Let's Encrypt

https://letsencrypt.org/about/

• How to Renew Your SSL Certificate in 4 Simple Steps (2022 Tutorial)

https://themeisle.com/blog/renew-ssl-certificate/

This could be alleviated should your Mac 'upgrade' later macOS.

So that can be an answer the basic issue. Or update certificates.