With systemctl restart php8.1-fpm you flushed opcache as well and forced it to be rebuild on the first incoming request. (Source: How To Clear PHP’s Opcache)
I would try to set in /etc/systemd/system/multi-user.target.wants/notify_push.service the following line
After=nginx.service php8.1-fpm.service mysql.service redis.service
And comment out or delete the second “After=redis.service” line.
When you forget nginx.service it should be that notify_push.service starts to run before the webserver = Nextcloud Server is up and running.