CI: use haystack-pydoc-tools package instead of local code

[masci]

Related Issues

• part of create API reference for core-integrations haystack-core-integrations#136

Proposed Changes:

Move the custom code to https://github.com/deepset-ai/haystack-pydoc-tools so it can be used from core-integrations and use the relative package instead

How did you test it?

locally tested without a readme api key

Notes for the reviewer

Checklist

• I have read the contributors guidelines and the code of conduct
• I have updated the related issue with new insights and changes
• I added unit tests and updated the docstrings
• I've used one of the conventional commit types for my PR title: fix:, feat:, build:, chore:, ci:, docs:, style:, refactor:, perf:, test:.
• I documented my code
• I ran pre-commit hooks and fixed any issue

[vblagoje]

LGTM, as it seems like a simple change. Please ask for a second opinion from someone with more context and knowledge of these tools - if needed.