test: verify all manifest schema parse with common python tools

[bollwyvl]

Description

Over on #1089, it was noted that the generated schema failed to parse with python-fastjsonschema. This is in particular a problem for pyproject.toml, as:

We can't use anything besides fastjsonschema, because it renders standalone .py files with no dependencies on any package, and those get vendored into setuptools. (Not for arbitrary tools, but only for setuptools and general schema) — @henryiii

References:

• JSON schema for pyproject.toml [tool.pixi] #1089 (comment)
• chore(deps): bump version to 2026.03.27 henryiii/validate-pyproject-schema-store#224
• no-op propertyNames causes invalid Python code to be generated horejsek/python-fastjsonschema#205

Changes:

• pixi.toml#/feature/schema/dependencies
  • bump pydantic
  • add/restore widely-used Python schema validator libraries
    • jsonschema
    • python-fastjsonschema
• schema
  • test_manifest.py
    • verify each generated schema can be parsed as a validator by each of the above libraries (in addition to jsonschema-rs)
  • model.py
    • base TaskName off NonEmptyString to force valid propertyNames in a number of places

      • appears to be a bug in pydantic where the pattern is discarded in propertyNames, but minLength works

How Has This Been Tested?

Checklist:

• I have performed a self-review of my own code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• I have added sufficient tests to cover my changes.
• I have verified that changes that would impact the JSON schema have been made in schema/model.py.

[ruben-arts]

Thank you @bollwyvl !