All network attached zero clients use the Elite Silicon Technology E2868/E3868 chip.
The free Linux driver available from their site is version 0.9.22 and requires understanding device ports internal to the zero client. Later versions, 0.9.34 and 0.9.57 exist, but only for rpm based distros such as CentOS 7. CentOS 8 now uses nftables instead of iptables so previous rpms will fail on an old dependency. 0.9.34/57 lock and unlock the whole zero client to a specific host server which is a more intuitive administrative interface.
All but the Phistek ZE7000 network attached zero client use the SMSC UFX6000/7000 USB to video chip for which there is no free Linux driver. It now uses the cheaper Displaylink DL-165 chip for 1920 x 1080 resolution. http://phistek.net/ze7000+.php Originally it used the more expensive DL-195 chip with 2048 x 1152 resolution and the web page still shows those older, higher specs. Both the DL-165 and DL-195 are supported by Linux.
If you have an HP T200 zero client with EST and SMC chips, you can attach a used DisplayLink device to one of its USB ports and Linux will see it. It would be nice to port the EST 0.9.57 package (build March 14, 2019) to support more modern Linux rpm and deb based distributions so that it would not be limited to the 5 meter USB cable length, but to 100 meter length of gigabit network cable.