The Parallel has a number of issues and generally isn’t a cart I can recommend. Here’s a guide on what carts are and aren’t recommended.

I think the only recommended plug & play option for PS2 is the RAD2X cable. It’s basically a stripped down console specific RetroTINK. I have one for my Saturn and it looks great.

And installation requires some pretty advanced soldering, so if you can’t do that then you’re looking over another $100 for a professional to do it.

Personally, I’m just sticking with the Carby HDMI adapter that I already have.