Consider upgrading to pydantic v2, removing pydantic v1 support

[andrii-i]

Problem

Need to support both pydantic v1 and v2 necessiates additional logic like pydantic_v1 module https://github.com/jupyter-server/jupyter-scheduler/tree/9d5e2ea50f5a9b1746c214fd7e4bb5f87fb768c8/jupyter_scheduler/pydantic_v1, adds dependencies, and improves codebase complexity.

Proposed solution

Upgrade to pydantic v2, remove pydantic v1 support

[dragonlobster]

compute_input_filename being defined twice keeps throwing an error for pydantic, i'm not sure how to fix it