There's also the extreme of simply storing the answer for each possible query as a u32 and just index the array, but there the overhead is much larger.
Rank-select is also interesting, but I doubt it comes anywhere close in performance.
I happen to also be working on a minimal perfect hashing project that has way higher throughput than other methods (mostly because batching), see https://curiouscoding.nl/posts/ptrhash-paper/ and the first post linked from there.