Yes, as Cosmic has stated, they are still available, but you actually have to go see the NPC to start the recruiting assignments. I think the cooldown got extended as well to 72 hours, but don't quote me on that.
For Fed, go to the building where the doff store contact is. There is another NPC there for the recruiting assignments. For KDF, the recruitment NPC is standing next to the doff store NPC below the platform.
The NPC for Doff packs can actually be a bit tricky to find in Starfleet Academy, as I found that standing slightly away from her desk only gave me the option to talk to Lt Ferra (who is on the opposite side of the booth). I had to walk all the way up to the desk to get the option to talk to the recruiter and start the Doff recruitment missions.
The Andorian and Tellerite officers are around the back of Lt Ferra's building, and the Vulcan officer is at almost the opposite end of the garden.