Support batch size scaling with dataloaders passed directly to `fit()`

Nobody has claimed this yet.

## 🚀 Feature
*This was first suggested/reported in #4000 and addressed in #4006 but then reverted in #4040 due to some GPU testing failure.*

Currently, batch size scaling cannot be used with dataloaders passed directly to `trainer.fit()` as exception is raised at:
https://github.com/PyTorchLightning/pytorch-lightning/blob/fe34bf2a653ebd50e6a3a00be829e3611f820c3c/pytorch_lightning/tuner/batch_size_scaling.py#L56-L58

The reason why this limitation was set is explained in #4006.
> This limitation was set in place, to secure that the user had a field self.batch_size that we could alter.
To remove this limitation we instead replaces the dataloader with a newly instantiated dataloader with altered batch size.

### Motivation

### Pitch

### Alternatives

### Additional context
- The limitation has been discovered in the current tuner revamp PR: https://github.com/PyTorchLightning/pytorch-lightning/pull/11089#discussion_r782849342.
- TODO after #11089 lands.

______________________________________________________________________

#### If you enjoy Lightning, check out our other projects! ⚡

- [**Metrics**](https://github.com/PyTorchLightning/metrics): Machine learning metrics for distributed, scalable PyTorch applications.

- [**Lite**](https://pytorch-lightning.readthedocs.io/en/latest/starter/lightning_lite.html): enables pure PyTorch users to scale their existing code on any kind of device while retaining full control over their own loops and optimization logic.

- [**Flash**](https://github.com/PyTorchLightning/lightning-flash): The fastest way to get a Lightning baseline! A collection of tasks for fast prototyping, baselining, fine-tuning, and solving problems with deep learning.

- [**Bolts**](https://github.com/PyTorchLightning/lightning-bolts): Pretrained SOTA Deep Learning models, callbacks, and more for research and production with PyTorch Lightning and PyTorch.

- [**Lightning Transformers**](https://github.com/PyTorchLightning/lightning-transformers): Flexible interface for high-performance research using SOTA Transformers leveraging Pytorch Lightning, Transformers, and Hydra.

cc @borda @justusschock @awaelchli @ninginthecloud @rohitgr7 @otaj @akihironitta

Start in pytorch_lightning/tuner/batch_size_scaling.py at the exception around lines 56-58, then review the behavior discussed in issues #4000, #4006, and #4040 and the tuner revamp context in #11089. The work is done when batch size scaling accepts dataloaders passed directly to trainer.fit() and uses a newly instantiated dataloader with the altered batch size without the current exception.

Written by the indexing model from the issue text.