onnxruntime

[CUDA][ROCm][Training] Fix cuda/rocm provider info hash (#19398)

When I test a new provider option, the training pipeline failed. I found
that training uses hash code of provider info to try get provider
instance. If a provider option is not used in hashing, the provider
instance fetched from cache might have different configuration for that
option.

Here I fix the hashing to use all provider options (except the default
Arena config that cannot be set from python API since training is used
with PyTorch in most cases).

Fixed a few obvious typo in the touched files.

Add regression test cases.