Use declarative validation API for validating text fields

[JasonWeill]

Problem

In #259 and elsewhere in the code, we apply custom, imperative validation rules to validate text inputs and generate error messages. This is more difficult to maintain.

Proposed Solution

@dlqqq in https://github.com/jupyter-server/jupyter-scheduler/issues/234#issuecomment-1298966576 recommends using Yup, Zod, or another validation library that can declare a schema and produce meaningful errors when input violates the schema.