Interesting approach. I just finished some work for a similar task in a different domain.
One thing that surprised me: tantivy's BM25 search is faster, more expressive, and more scalable than SQLite. If you're just building a local search (or want to optimize for local FTS), I would strongly recommend looking into tantivy.
If you have the resources, it would be very interesting to throw a some models (especially smart-but-context-constrained cheaper ones) at some of the benchmark programming problems and see if this approach can show an effective improvement.