Flush a live kernel box's files to the run store without stopping it.

The artifact pull calls this before enumerating its sources so the store leg holds everything the box does — otherwise files the periodic sync hasn't shipped only reach S3 at teardown, after the pull already ran. The run scope resolves from the notebook's own kernel config first (the box's identity — a caller-named session must never retarget another run's box), falling back to the caller's owned chat-session row for the detach case, and failing closed when neither answers: an unscoped flush of an isolated box would land its files on the shared base.