All you really need is a new cone washer-

$0.30.
Someone has wrapped teflon tape around the threads, which is worthless, as the washer (a.k.a. saniprene swivel seal)
at the bottom of this page.
A Sharkbite will use the same type seal, unless you go to a non-swivel female threaded fitting.
The problem with this connection is the water entry has brass male threads, the swivel type connection uses the soft washer, and the sharp metal on the inlet cuts the washer. If you wanted to replace the water inlet, you can buy one with female threads and a plastic close nipple, like the one on the left
here.