I cannot answer your question because I don't use that function. Hopefully someone who does will comment.
However, I'm not sure how encrypting or certifying messages by OpenPGP would help to avoid phishing, unless your contacts (who might be impersonated by phishers) use it too. The best defense against phishing is probably to thoroughly scrutinize any external URLs before opening them, and to use a plugin like NoScript in your browser that blocks any scripts from non-authorized servers.
I volunteer as a moderator to help keep the forum tidy. I do not work for Ritlabs SRL.
If anyone is interested, I got a response from the official support:
Hello, Thank you for contacting us.
We suggest you get GnuPG from https://www.gpg4win.org, install it and switch to GnuPG under the "Options\OpenPGP\Choose OpenPGP version" and under "Options\OpenPGP\OpenPGP Preferences -> Files -> GnuPG External Key Manager" sel ect C:\Program Files (x86)\Gpg4win\bin\kleopatra.exe.
Then access "Options\OpenPGP\OpenPGP Key Manager" and import the public keys of your recipients. And create your own key pairs for the needed email addresses.
The internal implementation of OpenPGP is outdated and now insecure, we have removed it fr om The Bat! v9
I am so glad that Ivan's reply from Support provided a link for Gpg4win, a Windows version of GnuPG. (There actually is a listing for Gpg4win on the GnuPG website, but there are so many software packages listed that I had overlooked it before.) It turns out that Kleopatra is downloaded along with Gpg4win (unless you uncheck a box).
It took a while to set up, but it actually was not too hard with these two resources. I hope that someday The Bat! Support will update the Help page.