If the spore drive is retired or otherwise classified Barclay wouldn't know about it.
Just like Starfleet crews of the 23rd and 24th centuries don't seem to have any knowledge of the conditions inside the old Delphic Expanse or the details of the NX-01's mission to find the Xindi weapon. The hearing where Archer briefed Admiral Forrest, Soval and others on the mission in the Expanse was ended with the testimony and data being classified and not for general consumption by the public or even other Starfleet officers or Vulcans.
Romulan cloaking technology of the mid-22nd century may fall into a similar category, as over a century later Kirk, Spock and the officers aboard the Enterprise don't seem to know what a cloak is or at the very least are baffled that the Romulans can now make some of their ships invisible. Historical records from the Earth-Romulan War appear to have been sanitized to an extent due to wartime censorship and security concerns. It seems that the Discovery's spore hub drive isn't the only thing featured in a prequel series that will be classified or forgotten by the time TOS rolls around.