Let's say I'm a level 7 Ardent/4 Ectopic Adept. That combination makes me, for all intents and purposes, a level 10 Ardent when it comes to manifesting powers. Would I, at that level, assume my 5th psionic mantle? Or would my PP/day and powers known advance without me picking up any new mantles? I thought I'd read somewhere once that you do still continue to assume mantles, but that doesn't make any sense. It doesn't seem like I would gain any more mantles (assuming new mantles being an Ardent class feature rather than a function of their power manifesting).
You do not get new mantles.
Anything that isn’t power points per day, manifester level, and powers known, you don’t get. Mantles don’t give you new powers known, they expand the list of available powers from which you may pick powers known, and are a separate class feature not covered by the prestige class advancement.
As an aside, note that ectopic adept’s only purpose is to partially-undo the Complete Psionics retro-nerf of astral construct. Note that this “retro-nerf” is not actually valid, by RAW (since errata rules specify that a supplement cannot overrule the primary source, only official errata can do that), and is almost-universally regarded as a terrible decision. It is fairly well-known that most of the team that worked on the Expanded Psionic Handbook did not work on Complete Psionics, and several of them have spoken out against some of its changes and poorly-implemented ideas (the divine mind, in particular, is a complete travesty that contradicts all existing psionics). While the ardent is widely considered a solid class, it’s one of literally three things in the book that are considered to be worthwhile (the others are the soulbow prestige class and the Practiced Manifester feat). Complete Psionics is frequently regarded as one of the worst books WotC published for 3.5, since it ruins both the fluff and mechanics of psionics, and is gratuitously heavy on stupid filler (fifty-some-odd feats named “[weapon type] Mind Blade” for instance).
I strongly recommend that your DM ignore the retro-nerf on astral construct, as it was completely unnecessary, and eliminate the ectopic adept as a thing. If you want a prestige class that focuses on astral construct, I suggest constructor, a far better-designed class.