I'm using Z16 for about a week and haven't seen any random restarts yet.
My setup is Ryzen 7 Pro 6850H, 32GB RAM, integrated 680M GPU, 1TB SSD, no WWAN and 1200p IPS non-touch.
Using BIOS 1.21 from within the 1st hour of operation.
I'm dual booting Kubuntu 22.04 and W11.
On W11 after the initial updates with the Lenovo utility the GPU driver wasn't working correctly, no correct resolution, lost brightness control etc Or W11 update caused this by overwriting the Lenovo provided driver. To fix it I tried reinstalling the Lenovo drivers from the device manager with no success. I then tried the drivers from AMD, but the install was failing and BSODed every time at a specific point. Finally, I used the DDU utility to remove all installed GPU drivers and tried to install the AMD one again. This time it succeeded, and I got back my brightness control.
Other than that zero issues on both Kubuntu and W11.
The battery could be better with moderate use. I see 7 to hours, I expected a bit more, maybe it's a bit early and the battery needs to charge a few cycles more for optimal performance. Or it's because I'm using kernel 5.15 on Kubuntu and power management for this new processor series is not optimal there. I want to use 5.19 but I have to wait for it to be available with HWE.
Overall I'm very pleased with this machine. The Z13 review here summarizes my experience. I'm glad I got it even though I was afraid of freezes/restarts or Linux issues based on what I read here or Reddit or Lenovo forums.