Loading from a checkpoint does not work properly in distributed training

Nobody has claimed this yet.

### Bug description

I train my model on multiple GPUs and save it with the `checkpoint callback` and `save_hyperparameters()`.
I get a directory which looks like this, so this part seems to work flawlessly:
```
/epoch=5
--/checkpoint
----mp_rank_00_model_states.pt
----zero_pp_rank_0_mp_rank_00_optim_states.pt
----zero_pp_rank_1_mp_rank_00_optim_states.pt
...
```

When I try to load the checkpoint with `MyModel.load_from_checkpoint()` on any of these files I only get errors. The tutorials only point me to some apparently outdated examples with a .ckpt file, which does not exist in these log directories.

Loading from the model directory does not help either.

When I load mp_rank_00_model_states.pt I get:

```
File "/.../projects/classifier_lightning/venv/lib/python3.10/site-packages/lightning/pytorch/core/saving.py", line 180, in _load_state
keys = obj.load_state_dict(checkpoint["state_dict"], strict=strict)
KeyError: 'state_dict'
```

When i load the other other files I get a lightning version error, even though it runs on the same environment.

So - how do I load my model from a checkpoint?

### What version are you seeing the problem on?

v2.2

### How to reproduce the bug

_No response_

### Error messages and logs

```
# Error messages and logs here please
```

### Environment

Current environment

```
#- Lightning Component (e.g. Trainer, LightningModule, LightningApp, LightningWork, LightningFlow):
#- PyTorch Lightning Version (e.g., 1.5.0):
#- Lightning App Version (e.g., 0.5.2):
#- PyTorch Version (e.g., 2.0):
#- Python version (e.g., 3.9):
#- OS (e.g., Linux):
#- CUDA/cuDNN version:
#- GPU models and configuration:
#- How you installed Lightning(`conda`, `pip`, source):
#- Running environment of LightningApp (e.g. local, cloud):
```

### More info

_No response_

cc @justusschock @lantiga

Start with MyModel.load_from_checkpoint() and the checkpoint-loading path in lightning/pytorch/core/saving.py, especially the _load_state failure at line 180. Compare the checkpoint callback output files under checkpoint with the expected .ckpt structure, and determine the documented or supported loading workflow for distributed-training checkpoints.

Written by the indexing model from the issue text.