Apply every queued mutation to disk, in FIFO order, until the queue is empty, then mark the worker idle. Spawned once via [`kick_worker`] and runs as the sole mutator; the awaited read paths wait on a [`Mutation::Barrier`] rather than draining themselves, so there is never more than one drainer. Consecutive appends to the same path are coalesced into one combined append. Each `createWritable` on
(inner: Arc<Mutex<Inner>>)
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