Unable to run custom sampler with custom arguments on TPU

Nobody has claimed this yet.

### Bug description

I'm trying to implement the meta-learning model following this [tutorial](https://lightning.ai/docs/pytorch/2.0.1/notebooks/course_UvA-DL/12-meta-learning.html). The tutorial uses a custom sampler with new arguments (e.g. N_way, K_shot, etc).

When I run the training on Colab TPU, it throws an error in this [file](https://github.com/Lightning-AI/lightning/blob/master/src/lightning/pytorch/utilities/data.py#L295). Looks like the new arguments cause the error because lightning expects the custom sampler has the same arguments as BatchSampler.

How can we deal with this?

### How to reproduce the bug

```python
https://colab.research.google.com/drive/1zZpHWE33ZkivrdfuoClZCp6cm2cJlKIP#scrollTo=c89b030b&line=3&uniqifier=1
```

### Error messages and logs

```
INFO: [rank: 0] Received SIGTERM: 15
File "/usr/local/lib/python3.9/dist-packages/lightning/pytorch/strategies/launchers/xla.py", line 107, in _wrapping_function
results = function(*args, **kwargs)
File "/usr/local/lib/python3.9/dist-packages/lightning/pytorch/trainer/connectors/data_connector.py", line 487, in _process_dataloader
dataloader = trainer._data_connector._prepare_dataloader(dataloader, shuffle=is_shuffled, mode=stage)
File "/usr/local/lib/python3.9/dist-packages/lightning/pytorch/loops/evaluation_loop.py", line 169, in setup_data
dl = _process_dataloader(trainer, dl)
File "/usr/local/lib/python3.9/dist-packages/lightning/pytorch/trainer/connectors/data_connector.py", line 200, in _prepare_dataloader
dataloader = _update_dataloader(dataloader, sampler, mode=mode)
File "/usr/local/lib/python3.9/dist-packages/lightning/pytorch/utilities/data.py", line 132, in _update_dataloader
dl_args, dl_kwargs = _get_dataloader_init_args_and_kwargs(dataloader, sampler, mode)
TypeError: __init__() missing 1 required positional argument: 'K_shot'
```

### 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 @carmocca @JackCaoG @steventk-g @Liyang90 @justusschock @awaelchli

Start with lightning/pytorch/utilities/data.py around line 295 and reproduce the failure using the linked Colab TPU example and meta-learning tutorial. Trace how the dataloader is reconstructed when the custom sampler uses N_way and K_shot; done means the custom sampler runs on TPU without the missing K_shot initialization error.

Written by the indexing model from the issue text.