[state_dict][7/N] Add a fine tuning e2e test case for distributed.state_dict and DCP (#111111)
As title
Differential Revision: [D50209732](https://our.internmc.facebook.com/intern/diff/D50209732/)
Pull Request resolved: https://github.com/pytorch/pytorch/pull/111111
Approved by: https://github.com/wz337
ghstack dependencies: #111106, #111107, #111275, #111109, #111110, #111120
