Save clipboard fallback images asynchronously and finish them before exit

[devmobasa]

Summary

Move clipboard fallback image saving off the event loop while ensuring that
accepted saves are not abandoned when the overlay exits.

Changes

Background saving

• Run file writes on a bounded, single-flight backend worker.
• Keep input handling and overlay updates responsive while a save is running.
• Capture immutable image bytes and the destination when a save is accepted,
  rather than looking up the current fallback later.
• Match completion results to their generation so an older save cannot clear
  or overwrite newer fallback state.

Reliable exit behavior

• Queue accepted saves as owned input effects.
• Drain those saves during common overlay teardown, including Save and Exit
  actions processed in the same event batch.
• Finish queued saves in order, even if an earlier save fails.
• Wait for accepted writes to finish before exit; this teardown wait has no timeout.
• Preserve unrelated effects when draining pending saves.

Failure handling

• Report save failures and retain unsaved fallback data for retry while the
  overlay remains active.
• Log exit-time failures and request a “Failed to Save Image” notification.
• Keep exit-after-save behavior tied to the matching successful completion.

Regression coverage

• Verify saved file contents, failures, retries, and single-flight admission.
• Cover stale completions and fallback replacement after save acceptance.
• Exercise immediate Save followed by Exit and teardown with a held writer.
• Verify FIFO ownership, unrelated-effect preservation, repeated teardown,
  and continued processing after I/O errors or worker panics.