Now that I've finally been able to download Mojave, I've discovered that the Radeon 7950 is not a supported Metal graphics card.
This may or may not mean that none of the cheese grater Mac Pros will ever be supported.
Or maybe that support will come in the future? That's not usually Apple's way of doing things.
I would definitely file a bug through the Apple Feedback Assistant application and make them aware that currently the AMD 7950 is not currently shown as being Metal compatible under System Information. Is your card a Sapphire HD 7950 Mac Edition? If so, I would contact Sapphire to see if they can inquire with Apple as well. Currently, their graphics cards are the ones that Apple lists under eGPU recommended cards.
Also, on the Apple Beta Software Program website, when listing Macs compatible with Mojave, they list this -
- Mac Pro (Late 2013, plus mid 2010 and mid 2012 models with recommended Metal-capable GPU, including MSI Gaming Radeon RX 560 and Sapphire Radeon PULSE RX 580)
I find this quite curious that Apple lists the MSI Gaming Radeon RX560 for the Mac Pro, which is not a supported GPU (RX560) when you are using an eGPU under High Sierra 10.13.4 (formally supported), and that is even more weird as Apple uses the Radeon RX560 in some models of the 21.5" iMac.
If I were you, I would try to make as much noise as possible with Apple using Feedback Assistant and through forums like this about support. Apple has stated publicly and formally that it is supporting the 2010 and 2012 Mac Pros with macOS Mojave, but has been fairly coy about what constitutes a Metal-capable GPU.
Should Apple not end up supporting the AMD 7950 GPU, the MSI model they listed can be purchased for $149.99 USD on Amazon, which is a pretty economical upgrade. It's not ideal, by any means, but it would allow you to upgrade to the latest version of macOS and put off contemplating a new Mac or WindowsPC at least one more year. Good luck!
Final note, for everyone - Apple is doing a poor job of articulating/documenting/validating the GPUs that it is supporting with respect to the Mac Pro 2010/2012 and supporting in eGPU enclosures. It's illogical to me that Apple supports the RX570/RX580 AND the RX470/RX480, but yet won't support the RX550/RX560. During the keynote, Apple emphasized the value of eGPUs to professional workflows (ironically enough, with DaVinci Resolve, and not FinalCut Pro X). If you're running an eGPU under Mojave, it would be interesting to find out if Apple has included the RX550/RX560 as supported cards at this point. Letting them know via Feedback Assistant is the first, best option, but certainly not the only option.