Running the pgsql query in production right now (3M indexed origins) takes
3 seconds.

'{}'::jsonb @> (metadata - '@context') looks computationaly expensive,
but it allows getting the number of non-empty metadata dicts in the same
scan as for the other ones.

As far as I know, postgresql does not offer an operator to test the strict
inclusion of the set of keys, so the only other way I can think of is to
test for string inequality with a second query.

Removing this sum() from the query, and sending:

select count(*) from origin_intrinsic_metadata
where metadata != '{\"@context\": \"https://doi.org/10.5063/schema/codemeta-2.0\"}';

as a second query results in two queries, which take 2 seconds and
1 second respectively.

And this is less correct (because the context value is hardcoded), hence
this implementation.