I think this sounds cool and internally-consistent.
I really, really like the idea about how manifesting takes strength, including, like, eyes to see or it being easier to interact/be seen by those close to you.
I will note that it sounds more like the perspective of an in-world scholar as opposed to the world-designer. Some things are unknown (like if a zombie's ghost is really bound to it or just too weak to do anything else), and that's fine. It gives wiggle-room for the DM and flexibility so you don't create an inconsistency by accident if a certain power doesn't make sense.

Can a ghost abandon a body? This sounds like one of the unknowns. At least, if it can happen, it happens rarely and it's hard to tell the difference between that and the body getting damaged enough to 'destroy' the undead.
Is a ghost hurt by its body being destroyed? I can see it being a shock, since the manifestation via their will is destroyed, and it perhaps destroying (or putting into slumber) the possessing spirit. On the other hand, I can see it just leaving the ghost exhausted and unable to act for a while, but not actually hurt long-term.
Maybe it hurts (most?) ghosts to abandon a body, willingly or due to damage, and that is why they are effectively bound as a skeleton or zombie once they become one: to stop being one would be to destroy oneself, and their will to 'live' is too strong to even consider that option. (If it wasn't that strong, they wouldn't have manifested in the first place.)

Does this make all undead sentient?
Or are some ghosts more-or-less emotional/memory echos of their past selves, instead of a true person. Mainly this is asking if your Laws allow for non-sentient undead, like mindless skeletons and zombies.
On the other hand, the end result might be minor. Just most dungeons of "mindless undead" are actually minded undead, but they are focused on the violence with which they died, or protecting the dungeon they guarded in life, so they act aggressive to anything that comes there.

What does this mean for magic? You mention 5e.
I can see spells like Create Undead and such help the ghost by empowering it with the magical energy, thereby making the manifestation easier. Perhaps in exchange the magic binds the spirit to the corpse, and the will to the creator of the undead.
Turn/Rebuke Undead powers overwhelm and channel the will of the undead, linking it to the user. (I forget how Turn works in 5e, but in 3.5 it had a chance to make them flee or destroy them.) If flee, it turns their focus to 'run away'; if destroy, it forces their will away from manifesting so that the possession fails, and the possessor (if not destroyed by that trauma--see earlier question) runs away.