Age doesn't do signing because PGP's signing mechanics have been one of the biggest fiascos in popular cryptography (to this day, mainstream PGP use via GnuPG doesn't produce authenticated ciphertext, due to confusion on the part of PGP's designers on the distinction between authentication and signatures). In day-to-day encrypted secure messaging, durable signatures are one of those things that sound great but are actually the opposite of what you want.

The most widespread practical use of PGP's signature capabilities are for package systems, where the actual contents of the package aren't confidential to begin with; PGP is only being used to sign. But PGP signatures are clumsy and archaic, and there are better tools to get the same capability without PGP's baggage --- notably the "signify" scheme that OpenBSD came up with and that minisign implements.