I had a similar problem yesterday but have figured it out and managed to rank up to Warrant Officer today. The naval rank missions are associated with minor factions and have the word "naval" in them but they aren't specifically called ascension or promotion missions any longer. Also, you can only do them if you have enough rep with the specific local faction that issues the mission - you might be Allied with the Federation but you still have to grind to Friendly with the local faction. So your Naval missions are probably all tucked away in the unobtainable section of the mission board.
I found a place where I still have enough rep with the local Feds and was issued a pirate hunting mission. However, the missions definitely are bugged in that the emails I got to tell me that I could obtain promotion and then that I have successfully completed the mission were both blank and had the wrong rank in the titles. Plus once I'd killed the 8 pirates in the nominated system, when I checked on my transactions panel the text for the mission had changed to tell me to go kill 4 pirates in a totally different system with no acknowledgement that I'd met my quota. I just went back to the mission giver and handed it in anyway and it worked OK.
So the process still works, but it's cosmetically broken.
I do have a big gripe with the new mission description in that it no longer tracks your tally of mission kills. I totally lost track of what progress I'd made as mission targets were hardly spawning in the Nav Beacon where I was hiding among the cops to avoid getting stripped and shredded. Loads of wanted smugglers and pirates but no designated mission targets. It took about 90 minutes to complete, I had no idea how many were left to do, and I was a bit punch drunk by the time I got out of there. That was just from dealing with Adders, Cobras, DB Scouts, etc.