Stores directory closures in an object store.
Notably, this makes use of the option to disallow accessing child directories except when
fetching them recursively via the top-level directory, since all batched writes
(using put_multiple_start) are stored in a single object.
Directories are stored in a length-delimited format with a 1MiB limit. The length field is a
u32 and the directories are stored in root-to-leaves topological order, the same way they will
be returned to the client in get_recursive.