I’ve long since moved on from Bazzite but the touchscreen worked. I had some sort of issue I never resolved that caused random freezes and reboots.
I’ve been on CachyOS for ~6 months now with zero issues other than my own tweak failures. I really like Limine and KDE. Touchscreen has worked well enough everywhere on the V3. Games are picky with it but I believe that is a Wayland/X11 vs gamescope issue. When in “gaming mode” using gamescope Steam it is fine. On KDE desktop for gaming the touchscreen is hit or miss.
Edit: for clarification of the post’s title. V3 is a tablet/laptop and “Desktop Issues” referred to being in the HTPC Desktop environment vs the Big Picture/Gamescope mode it boots into.