GRE-271: Document ASIAIR sync operations

[HeadCase]

Summary

• add a durable operator runbook for the repository-owned ASIAIR sync service
• keep acceptance procedures and dated deployed evidence in the verification document
• add README wayfinding for both documentation roles
• record completion of the manually verified obsolete-directory cleanup

Verification

• git diff --check
• sh -n deploy/asiair-sync deploy/tests/asiair-sync-test
• deploy/tests/asiair-sync-test

Linear

• completes the documentation follow-up for GRE-271
• GRE-225 remains open for the broader shared-host diagnostics and qualification work