Thanks for the report and sorry you ran into this, @johnrellis.
Please could you try this?
- Upgrade to Local 9.2.8, Apple Silicon version — you can download it directly from https://localwp.com/releases/.
- Quit Local.
- Open a terminal and run this:
rm -rf ~/Library/Application\ Support/Local/lightning-services/
- Start Local and try to start a site.
This will replace any old Intel binaries you had from the old install with new Apple Silicon ones and upgrade nginx to the latest version that ships with Local. (The latest nginx version should no longer show an error about the http2 directive.)