Refactor: Migrate `os.path` to `pathlib.Path` in `file_processor_handler.py`

[Dotify71]

Description

The airflow.utils.log.file_processor_handler module currently relies heavily on the os.path library for filesystem path manipulations.

To modernize the codebase, improve cross-platform readability, and align with modern Python standards, we should migrate these os.path calls (e.g., os.path.join, os.path.abspath, os.path.isdir) to their pathlib.Path equivalents.

Use case/motivation

Modernizing file_processor_handler.py improves readability and type safety by treating paths as objects rather than strings, which aligns with Airflow's broader goals of modernizing its Python codebase.

Related issues

None

Are you willing to submit PR?

• Yes I am willing to submit a PR!

Code of Conduct

• I agree to follow this project's Code of Conduct

[asthasoni22]

I'd like to work on this issue; could I get it assigned to me?