My Emacs (v29.1) was hanging when saving changes to .authinfo.gpg. Turns out, I ran into a known issue with a workaround. Downgrading gnupgp to a version older than 2.4.1 sorts things out.
I'm on macOS. Downgraded by downloading the 2.4.0 Homebrew formula at https://raw.githubusercontent.com/Homebrew/homebrew-core/59edfe598541186430d49cc34f42671e849e2fc9/Formula/gnupg.rb and installing with:
brew unlink gnupg
brew install ~/Downloads/gnupg.rb