[BUG] Frozen Parameters not saved when bf16 enabled but are when fp16 enabled

Describe the bug
When calling model_engine.save_checkpoint(), when bf16 is enabled frozen parameters will not be saved in the state_dict despite exclude_frozen_parameters=False by default.
Upon disabling bf16 training behavior reverts to normal.

To Reproduce
Steps to reproduce the behavior:
Train a model with vs without bf16

Expected behavior
A clear and concise description of what you expected to happen.
Frozen parameters should be in the state_dict

ds_report output

--------------------------------------------------
DeepSpeed C++/CUDA extension op report
--------------------------------------------------
NOTE: Ops not installed will be just-in-time (JIT) compiled at
      runtime if needed. Op compatibility means that your system
      meet the required dependencies to JIT install the op.
--------------------------------------------------
JIT compiled ops requires ninja
ninja .................. [OKAY]
--------------------------------------------------
op name ................ installed .. compatible
--------------------------------------------------
 [WARNING]  async_io requires the dev libaio .so object and headers but these were not found.
 [WARNING]  async_io: please install the libaio-dev package with apt
 [WARNING]  If libaio is already installed (perhaps from source), try setting the CFLAGS and LDFLAGS environment variables to where it can be found.
async_io ............... [NO] ....... [NO]
fused_adam ............. [NO] ....... [OKAY]
cpu_adam ............... [NO] ....... [OKAY]
cpu_adagrad ............ [NO] ....... [OKAY]
cpu_lion ............... [NO] ....... [OKAY]
 [WARNING]  Please specify the CUTLASS repo directory as environment variable $CUTLASS_PATH
evoformer_attn ......... [NO] ....... [NO]
fused_lamb ............. [NO] ....... [OKAY]
fused_lion ............. [NO] ....... [OKAY]
inference_core_ops ..... [NO] ....... [OKAY]
cutlass_ops ............ [NO] ....... [OKAY]
transformer_inference .. [NO] ....... [OKAY]
quantizer .............. [NO] ....... [OKAY]
ragged_device_ops ...... [NO] ....... [OKAY]
ragged_ops ............. [NO] ....... [OKAY]
random_ltd ............. [NO] ....... [OKAY]
 [WARNING]  sparse_attn requires a torch version >= 1.5 and < 2.0 but detected 2.1
 [WARNING]  using untested triton version (2.1.0), only 1.0.0 is known to be compatible
sparse_attn ............ [NO] ....... [NO]
spatial_inference ...... [NO] ....... [OKAY]
transformer ............ [NO] ....... [OKAY]
stochastic_transformer . [NO] ....... [OKAY]
--------------------------------------------------
No CUDA runtime is found, using CUDA_HOME='/usr/local/cuda'
DeepSpeed general environment info:
torch install path ............... ['/home/ethan/.conda/envs/od-train/lib/python3.8/site-packages/torch']
torch version .................... 2.1.2+cu121
deepspeed install path ........... ['/home/ethan/.conda/envs/od-train/lib/python3.8/site-packages/deepspeed']
deepspeed info ................... 0.13.3, unknown, unknown
torch cuda version ............... 12.1
torch hip version ................ None
nvcc version ..................... 12.1
deepspeed wheel compiled w. ...... torch 2.1, cuda 12.1
shared memory (/dev/shm) size .... 93.30 GB

Screenshots
If applicable, add screenshots to help explain your problem.

System info (please complete the following information):

• OS: Ubuntu 22.04
• GPU count and types 8xa100
• Interconnects (if applicable): unknown
• Python version: 3.10

Launcher context
using slurm torchrun

Start at model_engine.save_checkpoint() and trace how bf16 and fp16 training affect the saved state_dict, especially with exclude_frozen_parameters=False. Reproduce the comparison described in the issue and verify that frozen parameters are present in the state_dict when bf16 is enabled.