The description of the issue sounds like a drivers bug. While 10.12.6 should be supported, I did want to ask if it’s possible to check with Apple for Combo Updates which contain driver updates for the GPU.
When speaking with Apple make sure to ask about TimeMachine. That way if updating the OS/Drivers does not work, you can always revert if 10.12 is the preferred OS version.
Doubt Apple is pushing anything for that particular card under Sierra for his machine (one the system is long past EOL and two, that card didn’t exist when Sierra was EOL’d).
Probably will have to upgrade to Mojave (can’t upgrade to Catalina). Make sure your firmware is upgraded… the current firmware for your system is 144.0.0.0.0 and required for Mojave. You will get the latest drivers for Metal and your card that Apple pushed (which is still degraded by all standards) that were available during Mojave.
I suspect the only reason you are still at Sierra is for some software support (probably Adobe products).
Be forwarned… Mojave uses APFS as the filesystem and will reconfigure your boot drive to APFS. This filesystem is horrendous for HDD systems. Horrendous. Being a MacPro odds are pretty good you have multiple drives in your system. The install of Mojave will not convert your other drives, so you will want to uninstall WoW and Battlenet and reinstall them on one of your other internal drives. They will run far far far far better under MacOS Extended (i.e. HFS+).
Another option is to install Mojave on one of your internal drives and boot into that drive much like you would boot into Windows using bootcamp. The game itself doesn’t need to be on the same drive as the OS, it just needs the OS to drive graphics et al.
The full installer for High Sierra contains the firmware update. You run the installer and it then runs the firmware update. It adds two reboots to your already rebootalicious session when doing a full OS upgrade, but it should work. Just make sure you have either a Time Machine backup to revert to or you have a clone from something like Carbon Copy Cloner that you can use to clone back to your internal drive if the upgrade fails in any way.
Is your graphics card non-EFI or has it been flashed? You will likely need to use the stock video card that came with the system or an EFI flashed card in order to upgrade the firmware.
I had this problem under Sierra on my Late 2015 iMac with the AMD Radeon R9 M395 GPU. The problem turned out to be an outdated GPU driver (which WoW warned me about, once, a LONG time ago). Upgrading my iMac to Mojave resolved the problem.
To add to this here, our team is aware of some issues with liquid rendering issues with MacOS Sierra (10.12) with integrated graphics - and it has been replicated on Radeon R9 MXXX graphics cards as well. If it is an option, upgrading the operating system should resolve the graphical issues.