notebooks: persist compute block data filter values

Created by: rvantonder

Stacked on https://github.com/sourcegraph/sourcegraph/pull/32644

See three commits that hook up this functionality if you want to look at the code. This is more verbose than I'd "usually" do things, because I'm being defensive about JSON fields and anticipating changes/removals (making every field in option optional).

Test plan

Tested manually for this experimental feature