feat: refactor rest signer in fileio

### Feature Request / Improvement

Context: https://github.com/apache/iceberg-python/pull/2846#discussion_r2645920570

Currently S3 signer is tightly coupled with FileIO. This is awkward since the S3 Signer requires interaction with remote service (i.e. REST Catalog) and reuse its auth manager.

We can refactor here and create the signer in REST Catalog and pass to FileIO by overriding its `_load_file_io` function.

Also see [_init_sigv4](https://github.com/apache/iceberg-python/blob/a99dcada431a06329959cb7f71bf961343256bb0/pyiceberg/catalog/rest/__init__.py#L409-L459) for inspiration

Read the discussion in PR 2846 and the `_init_sigv4` implementation in `pyiceberg/catalog/rest/__init__.py`. Trace REST Catalog's `_load_file_io` path and how the S3 signer currently couples to FileIO. Done means the REST Catalog creates the signer using its auth manager and passes it to FileIO through the override.

Written by the indexing model from the issue text.