Keep Email backup cleanup owned by its parent shell #5824

🤖 Generated by the Agentic Engineer

Description

The Email backup refresh can lose its temporary workspace after stopping its completion watches. This blocks recovery checks and currently fails CI on #5820.

Steps to Reproduce

The native full Go regression in run 41607447333 failed the foreign unfinished-job control: the completion readback could not open its temporary file because its directory had disappeared.

Exercise the actual cleanup handler from a child process in the inherited-handler state, then verify the parent workspace still exists.

Expected Behavior

Only the owning parent shell may stop its watches or remove its workspace. Completed snapshot and mirror proof must remain required.

Actual Behavior

Cleanup has no process-owner fence. A cancelled watch can inherit the parent's exit trap before resetting it, matching the Bash maintainer's documented fork/termination race. The observed CI failure is consistent with that mechanism; a deterministic child-cleanup control is required.

Acceptance Criteria

• A real child executing the inherited cleanup handler preserves the parent's workspace and watch.
• Parent cleanup still stops and reaps its watch and removes its workspace.
• Existing source, owner, completion, mirror and privacy refusals still pass.
• Full native CI passes and the reviewed repair is delivered.

Related recovery work: #5578.