Every time I've used Lucene I have combined it with a SQL provider. It's not necessarily about one or the other. The FTS facilities within the various SQL providers are convenient, but not as capable by comparison. I don't think mixing these into the same thing makes sense. They are two very different animals that are better joined by way of the document ids.

SELECT * FROM benchmark_logs WHERE severity < 3 ORDER BY timestamp DESC LIMIT 10;

this index

CREATE INDEX ON benchmark_logs (severity, timestamp);

cannot be used as proposed: "Postgres can jump directly to the portion of the tree matching severity < 3 and then walk the timestamps in descending order to get the top K rows."

Postgres with this index can walk to a part of the tree with severity < 3, but timestamps are sorted only for the same severity.