So, I know that if my High Elf Wizard dies he goes to the chaotic-good afterlife plane or whatever. That's clear. He leaves a body behind, and gets a brand-new afterlife body in the chaotic good afterlife plane. So, what happens when he decides to plane shift back to the material plane with his afterlife body? Does he magically get resurrected to his material plane corpse or does he arrive with a brand new body? This is just the normal setting described in the PHB which I suppose is forgotten realms.
Although this has an answer for the Forgotten Realms, the “normal setting” in the PHB is not the Forgotten Realms and there is no canonical answer for just D&D 5e by itself.
The DMG goes into more detail about setting, but the basic concept is that the “default” setting of D&D 5e is mostly unwritten so that the DM can build it up from various pieces provided by the DMG (or their own homebrewed ideas). This applies especially to how the afterlife(s) and the planes work, which are explicitly undefined in the DMG and provided only as a collection of ideas the DM could use and customise, and the DM is expected to decide how things like death and afterlife work for their own game world.
So, that's your answer for the “normal setting in the PHB”: your DM is the one who decides these details, and there are as many answers are there are DMs. So consult your DM — or if you are the DM, decide how it works according to your tastes and preferences.
For the Forgotten Realms, the answer is that you're dead, and you can't leave your new planar home anymore without the permission and help of your god (or their agents). You are no longer a wizard or whatever, you're a “basic” soul of the form that the plane makes all new souls into (called a petitioner). You may or may not have memories of your past, also depending on who your god is and which plane they reside in. (That's assuming that you have a god. If not, you end up in Kelemvor's domain as a brick in the Wall of the Faithless, and you're staying there for eternity.)
As a meta-game aside, at this stage in your character's existence they usually stop being a player-character and are just a dead NPC.
If you somehow (potentially over aeons) achieved a higher level of existence than the basic soul — usually through exceptional service to your god — you may become some form of planar being that can travel back to the Forgotten Realms. However, by then you would not be a High Elf Wizard, you'd be an celestial or devil or whatever of some kind, with a planar body to match, with likely no concern for or even memories of your past life. There'd be no conflict with your old body, since it is no longer relevant to your existence. You certainly wouldn't inhabit it.
Your dead high elf wizard isn't a high elf wizard when he wakes up in the Upper Planes. He is a petitioner - identical in appearance and personality, but lacking the skills and abilities (and much of the memories) that he had in life.
A petitioner is essentially rooted in the plane it's arrived to, and can't be taken away from it; its ultimate fate is to fade away and become one with the plane or deity. In older editions of D&D, a petitioner that was being kidnapped from the plane would just reform somewhere else on it.