Am I right to assume that the query store of the JSON-API should be treated as an opaque blob?
Or in other words, if I know that queries commonly used by my use case would benefit from an additional index on the database, should I add it, or is this discouraged because there are no guarantees on the stability of the schema between SDK versions?
It is technically possible, but at this point in time we would discourage you of doing that, since the schema is not guaranteed to be stable. The query store of the JSON-API is used as an internal cache. If a schema upgrade is needed as part of an upgrade of the JSON-API, the existing schema is not taken into account and will be overwritten, which means you will lose your schema changes.