I believe this route with WASM is the correct one. WebSQL would have been tied to one single version of SQLite, with no alternative implementation.
With browsers adopting safe low level APIs like WASM and OPFS it enables a much broader range of databases to be available in the browser. We already have SQLite, DuckDB and various vector dbs.
OPFS is still under active development, but with some of the changes coming to it in 2024 it's going to become significantly better to use.
All of this is part of the enabling tech behind "local-first" apps. I'm somewhat biased as I work on ElectricSQL (we sync Postgres on a server to SQLite in the browser), but 2024 is going to be a supper exciting time for local-first software.