Even if no Rust code for it was seen during training, an LLM can trivially transpile SQLite's C codebase to Rust on the fly. For example, I just asked ChatGPT to write John Carmack's famous Fast Inverse Square Root algorithm in Erlang, without searching online or thinking, and it transpiled it immediately (while also extracting the knowledge in the same step). SQLite's semantics/code are stored in the middle layers of an LLM, and the last layers are able to convert it into any representation, as conditioned by the prompt. Cursor's experiment is deeply flawed because they merely extracted the model's compressed, lossy knowledge of SQLite's codebase and then just ran a bunch of tests/fixing rounds to make up for the lossiness. The claim that the agents built it from scratch is false.
Then you would expect the implementation to be structured the same as SQLite, and having glanced at the result, it looks like at least some things aren't. For example, it seems to use an operator-tree executor rather than SQLite's bytecode interpreter.