But is she a political officer, or is she in command of the region's military, thus making Rieekan under her command. The concept would have Rieekan as the base commander, while Leia is the Sector Commader. Making Leia equivalent to say and Imperial Moff or even Grand Moff, depending on how wider her command region is.
That would give way to her holding a General title by The Force Awakens. Though "General" is also a rank/title given to Jedi Knights and Master during the Clone Wars, while Padawan were given the title/rank of Commander. Note that Luke is called Commander Skywalker, while even Ahsoka Tano is called Commander Tano by the Clones, and later Kanan is called General by the Clones due to him being a Jedi. Could it be a subtle tell of Leia's Jedi powers?
So far as I'm aware the new canon books have indicated that Leia opted not to train as a Jedi, choosing instead to continue her political career in rebuilding the Republic.
On the one hand that is a little disappointing since I've wanted to see Leia as a full Jedi ever since that line in RotJ, but realistically I can see why they went that way. For one thing I doubt Carrie Fisher could physically sell it if it ever came to doing anything physical and from an in-universe perspective it makes sense for the character. Also from an in-universe perspective it's right that becoming a Jedi be an either/or proposition when choosing one's path in life. It always bothered me a little in the old EU where for some characters "being a Jedi" felt less like a life consuming ideology and more like a weekend hobby or fitness club or something.
As for any subtext of her using the title "General" over Princess, I think it has less to do with her embracing her heritage and more to do with her rejecting the politics and posturing of the senate. It also sends a message to those in the Republic with the wits to understand: "this is a war, whether you're ready to admit it or not."