They're not aiming at replacing SQLite-in-C with SQLite-in-Rust, they're doing this so they can implement more additional functionality faster than with C's chainsaw-juggling-act semantics and the inability to access the proprietary SQLite test suite.
See the features and roadmap at https://github.com/tursodatabase/turso
In other words, they are creating their own database and hitching on to the SQLite brand to market it. (That's fine though).
Without the test suite isn’t even more likely to have stability problems?
IMHO breaking free of SQLite's proprietary test suite is a bigger driver than C vs Rust. Turso's Limbo announcement says exactly that: they couldn't confidently make large architectural changes without access to the tests. The rewrite lets them build Deterministic Simulation Testing from scratch, which they argue can exceed SQLite's reliability by simulating unlikely scenarios and reproducing failures deterministically.