`Connection::get_stats` can result in `FsError` due to race with tantivy

`get_stats` operates directly on tantivy's index directory, so races can happen which result in `FsError(Error { kind: NotFound, message: "entity not found" })`. It's safe to ignore the error, however it might make sense to refactor that so the race can't happen.

Start at the Connection::get_stats entry point and inspect how it accesses tantivy's index directory. Reproduce or trace the race that produces FsError(NotFound), then confirm that the refactoring prevents the race rather than relying on ignoring the error.

Written by the indexing model from the issue text.