There's a lot of weirdness and myths and internet lore on the LS7's, that much is for sure.
Personally I have only observed the dreaded valve issue once out of probably 20 or 25 Z06's I've worked on in my life, and it was a 2007 model, which falls out of the common internet lore range of 2008-2011 cars being the worst affected. The fix was having the heads pulled and sorted out by Texas Speed where they got some nice new supporting parts and a nice CNC port job. That head work was about $1500 and ~10hrs labor if memory serves, we ended up installing longtube headers at the same time because it was really easy 'while we were in there'.
The rod issue is almost guaranteed to be a problem in the first 10k miles, so the majority of C6 Z06's out there have wildly exceeded this already or had the engine sorted out by warranty coverage. Beyond that it's just an awesome engine that loves to make power.
On your GS - catted 'green' long tube headers from Kooks, a good intake kit, and a tune is all you need. Honestly you'd need to go supercharged to get close to making the stock catback a meaningful restriction, and longtubes plus the stock catback make a great combo of snarly V8 noises without headache-inducing decibels or drone on the highway. Catted longtubes in particular are the best bet for this. After tuning you should see 40-60whp gain almost across the board with those changes, too.
You have a '19 Z06? That's a fantastic car! You're having traction problems, though, because those stock Goodyear all-seasons are more dangerous in dry weather with that stock ~550whp than proper R888R's or Pilot Sport Cups would be in the rain. My opinion, I am not a lawyer and all that, but I'm shocked so many OE's ship such powerful cars with such insufficient tires these days.
If there was ever a car that 100% transformed from just a set of proper tires, it's the C7 Z06. If you intend to use it as a summer fun car and not daily drive it or risk driving it in poor weather, I would strongly recommend a set of Pilot Sport Cups or R888R's. A good compromise though is the Michelin Pilot Super Sport or Michelin Pilot Sport 4S.
I'm spitballing a bit because I can't remember which of those tires are available in C7 Z06 sizing off the top of my head, but the takeaway is that a proper summer-only street legal motorsport tire is a fantastic improvement across the board for that car.
My hat's off to you, though - a C6 GS daily and a C7 Z06 garage beast is an absolutely fantastic pair of Vettes to own.