It really depends what you mean by "necessary to the story". Sephiroth has so many gaps in what make him like he is in the OG. Particularly when it comes to *why* he reacts how he does to the information in Niblehim. It is... very obvious something was missing there. What that something originally was? I don't know.
Nojimia (the guy who wrote Sephrioth in the first place!) decided Sephrioth was missing two friends he didn't mind hanging out with. Who found out the truth of their origins first and then in trying to find out what happened to make them leave Shinra (and betray him), Sephiroth stumbles across his own origins. And that is after he spent two years dealing with SOLDIERs turned into monsters via Jenova's abilities.
The trouble I have with Sephiroth *before* he goes crazy in the OG is that there is no context to figure what is "normal" for him that would make the existance of Jenova abnormal. Or the story he reads of Project S. As it is, he's extremely cool-headed right up until he goes into the Mako reactor. So this gives the impression of a usually calm person snapping out of nowhere... which... always feels kinda hollow from a character motivation perspective.
The two big hints we have for *why* Sephrioth goes crazy in the OG is the line of Cloud (remembering Zack) that leads Sephrioth to think he's the same as the makonoids. And Sephrioth's admission that he has always felt special and different from other people ever since he was little.
Cloud (Zack)
Wh... what is this!?
Sephiroth
Normal members of SOLDIER are humans that have been showered with Mako.
You're different from the others, but still human.
But, what are they? They've been exposed to a high degree of Mako, far more than you.
Cloud gets to his feet.
Cloud (Zack)
...is this some kind of monster?
Sephiroth
Exactly. And it's Hojo of Shinra that produced these monsters.
Mutated living organisms produced by Mako energy. That's what these monster's really are.
Cloud (Zack)
Normal members of SOLDIER? You mean you're different?
Sephiroth clutches his head as though in pain.
Cloud (Zack)
H... hey, Sephiroth!
Sephiroth
N... no......
...Was I?
He starts slashing at the pods with the Masamune, and Cloud leaps back.
Sephiroth
...Was I created this way too?
Am I the same as all these monsters......
Cloud (Zack)
...Sephiroth.
Sephiroth
You saw it! All of them... were humans...
Cloud (Zack)
Human!? No way!
Sephiroth
...I've always felt since I was small...
That I was different from the others. Special, in some way.
But... not like this...
Am I...... human?
This indicates that (a) Sephrioth had yet to really think about himself being one of Hojo's "science experiments" and (b) Sephiroth has always known he's not like other people... even when he is sane. He *likes* being different and special. This comes out later in Nibelehim when Sephrioth is faced with the reality that he really was just another science experiment to Hojo. However, what we are missing in the OG here is... why Zack would pay attention to the subtle difference between how Sephrioth talks about different kinds of SOLDIERs... and why Sephrioth would make the leap from "the makonoids" to "used to be human" to being "the same as all these monsters". All with the one question of "you mean you're not a normal member of SOLDIER?"
We've barley run into any SOLDIERs in the OG yet... and all of them look and act a lot more human (including Cloud!) then several other Shinra enemies. I'd... think Sephiroth was crazy is a very different manner (this is logical to you because.... why?) if the information we learn after this isn't such a part of general FFVII lore by now. Even then, the information we learn in the Manor still doesn't explain how Sephrioth made that logical leap in the OG. The experiment it describes to make him is nothing like the makonoids.
And this why the argument of "Genesis drove Sephrioth crazy" has never really sat well with me. Crisis Core uses the exact same dialogue at the Nibelehim reactor there. Genesis isn't even on the scene yet. If anything, Crisis Core doubles down on the reality that it was Zack's question that sent Sephiroth over the edge! Why yes, I am a proponent of the theory that it was Zack who is the most... immediately... at fault for driving Sephrioth crazy.
Genesis only shows up at Nibelheim once Sephrioth is already questioning if he's human or not. Genesis himself has.... nothing to do with Sephiroth coming to that realization that he's not human at Nibelehim. And for that matter... Sephrioth doesn't care what Genesis is talking about. He rejects it and goes on to read the information in the Manor like in the OG and *that* is the information that really sticks with him.
What Genesis at the Nibelehim Reactor does is make *sure* the player knows Sephrioth actually knows what Jenova really is. Which... isn't actually specified in the OG. It's heavily implied when Sephrioth say he's absorbed the "Knowledge of the Ancients" from the Lifestream... but he never actually comes out and says something to the effect of "my mom was actually the Thing from space who crashed on the Planet and decimated the Cetra... and who was then found 2,000 years later and experimented on by Shinra". It's... not until ACC that we really get hard confirmation that Sephrioth (or rather, his Remnants) do know what Jenova was/is.
For me, Genesis (and Angeal) are "necessary" to the story of FFVII in that they provide a wealth of context for Sephrioth's breakdown at Nibelheim. You've now got two years of Sephrioth seeing SOLDIERs getting transformed by *something* in mako tubes into something that isn't human. And Sephrioth himself has been looking into Project G and realized that it's weird and off and *did something* to Angeal and Genesis that changed them. Zack also has learned *way more* about Project G than even Sephrioth has to the point he found out Jenova Cells were involved to make Genesi and Angeal. And Sephrioth was not around for that conversation...
They bring context to Zack asking Sephrioth if he's a "normal" SOLDIER... Zack knows Genesis and Angeal were not normal... and since it sounds like Sephrioth doesn't think's he's a "normal" SOLDIER, Zack wants to know if Sephrioth might be like Genesis and Angeal. Who are liked with Jenova who's name is on the wall of the reactor... and Zack *knows* Jenova has to do with why Genesis and Angeal went crazy.
They explain why Sephrioth see the monsters in pod and thinks that they might be human... he's been seeing human-based copies for all of CC; if they *look* human-shaped in a mako pob, then they probably started out as one. And they explain why Sephrioth woudld think about Hojo being involved with himself for so long and realize he might be an experiment as well. He knows Hollander was involved with how Genesis and Angeal were... created... and is why they themselves are not "normal" SOLDIERs.
All this comes together to give reasons and context for why Sephrioth comes to the realization that he is not "special" at Nibeleheim. He is not the only "non-normal" SOLDIER anymore. And he needs to be "special"... so he goes looking for a way to be "special" again... and finds it in the (wrong) reports about Jenova being a Cetra in the Nibelehim Manor. And those reasons and context help a lot to make Sephrioth feel much less "random" as a character when it comes to his motivations at Nibelehim.
Now... I'm not going to say that Nojima could not have come up with some other scenario to explain why Zack asks the question he asks or why Sephrioth reacts the way he does. But to say that Genesis (and Angeal) aren't necessary is... going a bit too far. It's like saying any information outside of the bare-bones of "what happens" in a story isn't "necessary" either. People *usually* like finding out more world-building and background info on why people do what they do in stories. It makes for a "fuller" world. And the number of "things/rolls" in FFVII that Genesis and Angeal fill with what they do (from a narrative perspective) is... substantial.
And this is all just from a practical "what does Gensis' actions actually do in the plot" angle. This doesn't get into anything related to how Genesis functions as a way for the devs to give commentary on the themes they want people to pick up on in the game...