`log_dir` contains both forward and backward slashes as path separator when using remote file location as `default_root_dir` on windows

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### Bug description

I am running on Windows OS and storing logs and artifacts on remote location (AWS S3).

```python
path_pl_logs = f"s3://{bucket_name}/pytorch-lightning-logs/{experiment_name}"
trainer = pl.Trainer(
accelerator="gpu",
devices=1,
max_epochs=checkpoint_n_epoch,
default_root_dir=path_pl_logs,
)
```

With the following output containing a mixture of forward and backward slashes. This causes problems with the folder structure.
```python
trainer.log_dir
>> s3://{bucket_name}/pytorch-lightning-logs/{experiment_name}\lightning_logs\version_0
```

Ideally when using a remote location it would not use os.path.join to create folder/filenames but instead just use a forward slash file separator.

### 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): Trainer
#- PyTorch Lightning Version (e.g., 1.5.0): 2.2.1
#- Lightning App Version (e.g., 0.5.2):
#- PyTorch Version (e.g., 2.0): 2.2.2
#- Python version (e.g., 3.9): 3.11
#- OS (e.g., Linux): Windows 11
#- CUDA/cuDNN version: 12.1
#- GPU models and configuration: NVIDIA RTX A2000 Laptop GPU
#- How you installed Lightning(`conda`, `pip`, source): pipenv
#- Running environment of LightningApp (e.g. local, cloud): local
```

### More info

_No response_

cc @justusschock @lantiga @borda

Start at the Trainer.log_dir path construction used when default_root_dir points to an S3 location, and inspect how Windows path separators are applied to the remote path. Done means the resulting remote log path uses consistent forward-slash separators instead of mixing forward and backward slashes.

Written by the indexing model from the issue text.