There have been some DCT issues. More than GM would like, to be sure. But consider that there have been some 50,000 to 60,000 C8s produced and sold. If even 10% of those had transmission issues, the Corvette forums would be inundated with nothing but faulty DCT posts. Most owners don't seem to have any problems with the DCT.
In the early production DCTs, there were problems with porous castings in a part called the valve body that caused leaks in some cases. That was resolved. There have been gasket leaks where the pan on the bottom of the DCT attaches to the DCT case. The unit was redesigned with a cast pan that seals with an o-ring rather than a gasket. But both of those issues seemed to affect only a relatively small number of units.
There have been [unproven] reports that some problems have been caused because a supplier of components to Tremec wasn't properly cleaning the parts, and debris was getting into the DCT. While unconfirmed, the fact that GM has added a "flush" procedure to the DCT filter change (the procedure forces the DCT fluid to circulate through the filter for 8 minutes prior to the filter being changed. It's not a traditional flush and refill), and asked dealers to ship used filters back to them for study seems to support this.
But the important part is that the vast majority of owners don't seem to have these problems.
And there's no difference in the DCT between the Z51 and base. The transfer gears between the engine and transmission are different, and the Z51 has an electronic limited slip differential, but the DCT itself is identical: same clutches, same gears, same valve body, same everything.
I'm at 6400 miles on my 2021, and the DCT is fine.