How can prompt engineering reshape pm methodologies, Agile?

Based on your to do ("backlog") tasks, have it point out which tasks need beter task descriptions. That would be an agenda for a planning meeting. Or have it turn yesterday's Slack traffic into an agenda for a daily status meeting if you do those. "Ceremonies" without prepared agendas are a huge time sink.

It can provide more documentation and a ready-to-adapt process.