Can I install Monterey on my MacBook Pro Retina late 2013?

Sorry, no. Big Sur is the latest possible macOS version for a late 2013.

Also see the following from Identify your MacBook Pro model - Apple Support

MacBook Pro (Retina, 13-inch, Late 2013)

Model Identifier: MacBookPro11,1

Part Numbers: ME864xx/A, ME865xx/A, ME866xx/A

Newest compatible operating system: macOS Big Sur

Instead of using an outdated Safari version that doesn't have current security updates, 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/

If Web Browsers need to be used other than Safari

Browsers by Mac operating system

Though, I personally stay away from Google Chrome as it is always calling home with all my user browsing history and what Google does with that Info - it is believed they use that info for Other Purposes which are not always Transparent

Might try this, it's Chrome Browser without google & without Ads...

https://brave.com/