Just watch the screens of anything the companies use when you're in there. Look at the model numbers and Google them. You'll find a lot given most aren't that creative: they do a customized version of the default, enterprise offering.
For instance, a restarting computer at the local Kroger where I shop said IBM SurePOS. Looking it up, it turns out some group tried to make a concurrent version of DOS that IBM modified into a specialized OS for POS's. Recently, they upgraded to touchscreens running Linux on Fujitsu boxes. The GUI is ugly, slow, and has the tell-tell coffee mug in corner of dialogs. Appears Kroger, always slow as can be, got on Java desktop bandwagon just as everyone else chasing fads were leaving it for stuff like web apps or Electron.
The self-checkouts have a Windows loading screen. Probably was WinXP Embedded given they're old. The handhelds use mainframe-era, terminal apps. Their computers at customer service are thin clients from HP at this location. I think one said "Iceweasel" one time. The checkout predictor thing with the three balls on monitor showed something Linux-related one time. If you ask employees, you'll get SCO OpenServer, AS/400, mainframe, and a pile of random apps with web interfaces. I don't know what they run. One employee told me email and web browsers load in what must be VM's that take 5-10 min to load on the thin clients. It must be unbearable.
So, Kroger certainly uses plenty of Linux with mission-critical services being on it. Their choices for inventory and desktop GUI's also hint they're pretty backwards in their practices. I'm not sure about the others since I mostly shop at Kroger.