I am experiencing a similar problem. I have a Tesla K40c with cuda compute capability 3.5. Since Mathematica 12.2, the NetTrain with TargetDevice->"GPU" doe not work (NetTrain::mxoldgpu: Your GPU does not support the operations required to evaluate this network). Regarding the documentation, only cc 3.7+ is supported.
Is there any specific reason for that? Is there any chance that Wolfram will fix this issue?
The only technical difference between 3.5 and 3.7 is 48K of shared memory per multiprocessor (the cc 3.7 has 112K, but the newer 5.0 has 64K, which is not much different). Ok, 3.7 also has 128K of 32-bit registers per multiprocessor, but it is a kind of outlier since all the newer cc 5.0+ has 64K (same as cc 3.5).
The features and specifications are the same for cc 3.5 up to 5.2.
The mxNet requires the compute capability 3.0 and higher (https://www.nvidia.com/en-sg/data-center/gpu-accelerated-applications/mxnet/)
I am so sad that I cannot use this powerful card anymore, especially when there is no technical reason for that.
I think if there is a way to do some hack to override the cc version detection (simulate the higher version), or if Wolfram could fix it in the future releases.