Add data assimilation docs, validation, and tests

[kruparell]

Follow-up to #329–#345: user-facing material for the data assimilation (DA) feature, plus two small core hardenings and 16 tests.

[grey-nearing]

Thanks @kruparell! Since the upcoming UI will replace the need for the notebook tutorials (and we plan to remove tutorial/ to keep the repository lightweight), we moved all tutorial/ commits from this PR over to Draft PR #351 so none of that work is lost, and kept all of the documentation, validation improvements, and unit/integration tests here on #352 to merge into main.