Lightning+DDP: use_distributed_sampler=True always shuffles data in DDP despite using custom sampler

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### Bug description

When using PyTorch Lightning Trainer in DDP with `use_distributed_sampler=True` and providing a custom sampler to the dataloader, the sampling order from the custom sampler is neglected. Instead, data is always shuffled.

One can track this issue down to [this line](https://github.com/Lightning-AI/pytorch-lightning/blob/634e6e6d06fced4cacfb9de675fc328ace1a06c4/src/lightning/pytorch/trainer/connectors/data_connector.py#L243) where the custom sampler is wrapped with a `DistributedSamplerWrapper`. However, the kwargs contain `shuffle=True` due to [this line](https://github.com/Lightning-AI/pytorch-lightning/blob/e55650dcebe1cb9c50addab06d292a1704b1d288/src/lightning/pytorch/trainer/connectors/data_connector.py#L490).

When using a custom trainer in combination with fabric as suggested [here](https://github.com/Lightning-AI/pytorch-lightning/tree/master/examples/fabric/build_your_own_trainer), the sampling order from the custom sampler is respected. The reason for this is found [here](https://github.com/Lightning-AI/pytorch-lightning/blob/e55650dcebe1cb9c50addab06d292a1704b1d288/src/lightning/fabric/fabric.py#L398) where fabric does not pass `shuffle=True` as keyword argument.

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

v2.5

### Reproduced in studio

_No response_

### How to reproduce the bug

```python
from torch.utils.data import Dataset, Sampler, DataLoader
import lightning as L
import torch.nn as nn
import torch

class IntegerDataset(Dataset):
def __init__(self):
self.data = [i for i in range(100)]

def __len__(self):
return len(self.data)

def __getitem__(self, idx):
return {"data": torch.tensor([self.data[idx]])}

class InOrderSampler(Sampler):
def __init__(self, dataset):
self.dataset = dataset

def __iter__(self):
yield from range(len(self.dataset))

def __len__(self):
return len(self.dataset)

dataset = IntegerDataset()
sampler = InOrderSampler(dataset)
dataloader = DataLoader(dataset=dataset, batch_size=3, sampler=sampler)

class MyModule(L.LightningModule):

def __init__(self):
super().__init__()

self.layer = nn.Linear(10, 10)

def training_step(self, batch, batch_idx):
print(batch)

input = torch.randn(10, 10, device = self.layer.weight.device)
output = self.layer(input)
loss = nn.functional.mse_loss(output, input)
return loss

def configure_optimizers(self):
return torch.optim.Adam(self.parameters(), lr=1e-3)

model = MyModule()

trainer = L.Trainer(
max_epochs=1,
use_distributed_sampler=True,
)
trainer.fit(
model=model,
train_dataloaders=dataloader,
)
```

### Error messages and logs

The integers from the dataset are not printed in order, but are randomly shuffled.

### Environment

Current environment

```
pytorch-lightning 2.5.1.post0
torch 2.7.1
torchmetrics 1.7.0
torchvision 0.22.1
```

### More info

_No response_

cc @justusschock @tchaton

Start in src/lightning/pytorch/trainer/connectors/data_connector.py at the linked sampler-wrapping and kwargs lines, then compare the corresponding logic in src/lightning/fabric/fabric.py. Reproduce the behavior with the provided custom sampler and DDP example; done means the custom sampling order is preserved when use_distributed_sampler=True.

Written by the indexing model from the issue text.