doc: tutorial updates for 3.0

[jhamman]

This is a work in progress. Running through the tutorial helped identify a number of issues that we likely want to address before we release 3.0.

TODO:

• [ ] Add unit tests and/or doctests in docstrings
• [ ] Add docstrings and API docs for any new/modified user-facing classes and functions
• [ ] New/modified features documented in docs/tutorial.rst
• [ ] Changes documented in docs/release.rst
• [ ] GitHub Actions have all passed
• [ ] Test coverage is 100% (Codecov passes)

[dstansby]

Woop woop! In case you don't know about it already, https://github.com/scientific-python/pytest-doctestplus?tab=readme-ov-file#fixing-existing-docstrings might be helpful

[jhamman]

closing in favor of #2589