Safe log rotation and backup verification in bash

Write a bash script for Ubuntu 24.04 that: rotates application logs in /var/app/logs older than 7 days into dated .tar.zst archives under /var/app/archive, deletes archives older than 90 days, then verifies last night's Postgres dump in /var/backups/pg (newest .dump file) by restoring it into a throwaway database on the local server, running a row count on a table named in an argument, and dropping the throwaway database. Exit non-zero with a clear message if the dump is missing, older than 26 hours, fails to restore, or the row count is zero. Log to stdout with timestamps. Must be safe under set -euo pipefail, must not delete anything outside the two directories even if a variable is empty, and must hold a lock so two copies cannot run at once. Return only the script in one code block.