Clean up failed checkpoint writes

[im-kvijay]

Proposing a focused cleanup fix for #3646. Checkpoint staging currently uses a temporary index but writes packs into the shared object store, where failures can leave temporary files behind.

Each capture would own its index and new objects, then publish completed objects before its hidden ref. Failed staging removes only its own storage; Git's temporary-directory prefix lets normal pruning reclaim stale crash leftovers. Snapshot contents, the user's index, and the 30-second deadline stay unchanged.

The implementation has 68 passing focused tests, including three cleanup regressions that fail upstream, plus typechecks and targeted lint/format checks. It touches five files with 114 effective non-test changed lines (size:L). In a local 2,000-file fixture, capture medians changed from 30.6 to 32.0 ms for 10 modified files and 90.0 to 118.5 ms for all files modified.

This addresses staging debris, not long-capture scheduling. Pack/index publication can still fail partially, and private storage adds an alternates level. Related #4338, #8301, and #4517 remain unmerged. Implementation for review: #9809.

Created with GPT-6 in Codex.