And this, kids, is a good example of why homebrew is not a real package manager, and why macOS is not the best at running production services.

I hope you have a backup somewhere else, not on the Mac Mini. One option would be to restore it on another machine on Postgres 14, follow the upgrade path to 17 (idk if you can jump directly but a few Google searches will cover this), verify the data, back up the new db, somehow upgrade Posgtres on your Mac, and restore the new back up. Done.