Overhaul docs build chain

[bollwyvl]

References

• as suggested on Fix registry state lookup #3653 (comment)

Problem

The docs don't currently build.

Suggested Improvement

• use myst-nb
  • under more active development than nbsphinx, and provides some nice features
  • some of its typographical features translate nicely into the lab experience with jupyterlab-myst
  • has better notebook execution caching for iteration
  • has better observability of failures and options for executing notebooks
• use pydata-sphinx-theme
  • better use of screen real estate
  • slightly more complex to get a good nav structure
• use jupyterlite directly vs jupyterlite-sphinx
  • allows for sphinx 5 (jupyterlite-sphinx pins to <5, don't know or care why)
  • would allow building the lite demo without the full docs site
    • which takes a long time, though that would be helped above
• add typedoc
  • i've been using a markdown theme, and then having myst-nb take care of it
    • this allows typescript APIs to be discoverable in the unified sphinx search
      • even though the output is somewhat suboptimal