Apple introduced the Hide My Email feature with macOS Ventura in late 2022. Hide My Email is built in to Sign in with Apple and iCloud+.
GPG Mail 7.1 introduced support for OpenPGP encryption and signing of emails using the Hide My Email service. By default Apple disables S/MIME encryption when users switch to a Hide My Email address.
In order to use OpenPGP with your Hide My Email address, please create a new key in GPG Keychain using that exact email address. When composing a new draft, GPG Mail will look for a key matching the address and when a key exists for one of your Hide My Email addresses, show the encrypt and sign buttons.
When no key exists matching the email address the buttons will not be visible.