So say being master of death would include death deities how do you think there relationship with Harry would be?
I don't think being the MoD has anything to do with any death dieties — mostly, because I don't think these dieties exist in the HP universe.
I already talked about the MoD here and here, and about Necromancy in HP in general here. But it always seemed to me that true Necromancy doesn't really exist in HP (it's telling its most advanced form of it is Inferi, which don't even count as 'alive'. I truly believe Voldemort lied to Harry when he offered to allow him to talk to his parents in first year. Harry was right), and that Death, as portrayed in the Tale of the Three Brothers, isn't real. Beings like that just don't fit with the worldbuilding we see. I see Death in the story more like how people talk about the Angel of Death or the Grim Reaper — usually as more of a figurative concept, an artistic rendition of personified death, rather than a being they really believe exists. As such, Harry wouldn't have a dynamic with any death deity, I just don't think there are any in HP.
(Obviously, you can headcanon death deities and write them in fic, I just don't think it makes sense with the world as shown in the books)
I don't think being the MoD actually gives him that many new abilities or anything, all things considered. Like:
He'd be the master of all 3 Deathly Hallows (so he'd have the wand, the stone, and the cloak with all their capabilities)
He wouldn't die until he chose to. And he will choose to die eventually. Like Ignotus Peverell. (talked about it more in the first post I linked).
Some limited access to the veil. As in, he could step into the veil and come out alive. I believe he could've pulled Sirius out if he went in immediately after Sirius died, but he won't be able to bring back anyone else due to how Sirius died, which was kind of unique, magic-wise. (talked about it more in the first post I linked).
General resilience to harmful spells. I low-key think Harry's ability to resist the Cruciatus is related to his MoD status. After he dies in the forest, he can resist it, he can not feel it: "He was lifted into the air, and it took all his determination to remain limp, yet the pain he expected did not come." (DH). So, yeah.
And that's like it, really.
I like to think of the MoD as something more subtle. I like to think all these skilled wizards (Voldemort, Dumbledore, and Grindelwald) who searched out the Hallows would have been disappointed were they to truly master them all. They were arrogant, theatrical, and loved showing off in ‘bangs-and-smells’ magic. The duel between Voldemort and Dumbledore at the end of OotP is a good example of their tendency to show off. Of their need for everyone to know they are the best and greatest.
Harry isn't like that though. Harry doesn't have that need, and that's why he is the Master of Death. I like to think that like Harry's more subtle talent and skill, the MoD's abilities aren't impressive at first glance. They aren't ones the likes of Voldemort or Dumbledore will see as impressive enough, they will be let down by what it means to be the MoD — but not Harry. For Harry, it would be too much, more than he ever considered wanting, but that he'll happily take and use it if it can help him protect himself and the people he cares about.
So, thematically, I just really like the idea of being the MoD not actually meaning much. Yes, it keeps you alive, but you aren't actually the master of death. You can't do necromancy or have any special abilities beyond what the Hallows allow. I love the idea that if Voldemort, Dumbledore, or Grindelwald actually became the MoD, any of them would have been disappointed because they expected more. But Harry will take what he can get, because he didn't even expect that much, yk?
(I just love the more tame not op version of being the MoD because of the themes. It's still impressive, resisting the Cruciatus is impressive, Immortality is impressive, it's just not an in-your-face impressive, but it doesn't need to be. It doesn't need to be more. Mastering death is about accepting you will die and that immortality wouldn't last forever, just until you are ready.)
So, yeah, these are my opinions on the MoD stuff and why I like to keep the abilities simple and straightforward in my own headcanons. I think it works better with HP's lore and with the book's themes. It also fits Harry's character better, Harry, who prefers Expelliarmus or Stupify or any other "lame spell" because they are effective. He doesn't need his spells to be impressive, he needs them to work.