My theory about the referenced third Shinjou brother (whom I’m calling Souma, spelled with 瀧 [waterfall]—to go with the 柊 [holly olive] and 涼 [cool breeze] in Touma’s and Ryouma’s names respectively, both thematically and pronunciation-wise—and the same 真 [truth] as in his brothers’) is that he’s Touma’s twin.
He can’t be older because when you have a child but can’t take care of them (and if Souma and Touma are different ages, then the younger was probably unplanned), you give up the one who was just born, not the one who’s already a year or two old. It would fit with Touma’s being unaware of his existence, but it makes the least sense.
It’s possible he could be younger, then, since their mother says that the one she wanted to keep was Souma. I’m pretty sure you have to be 6 or older to be diagnosed with autism (although, that’s in the U.S.; idk how or if things are different in Japan), but I don’t know how young signs of neurodivergence become apparent, but for Touma to not remember Souma, to not be aware of his existence, he had to have been pretty young, no more than a couple years old, when Souma was born. (Though, well, I don’t think it actually matters whether she knew Touma was different at the time, but more on that in a bit.) It’s certainly not unlikely that Souma’s younger, but I think it’s more likely that they’re twins.
I don’t know if they’re identical (Souma’s definitely also autistic) or fraternal (Souma may or may not also be autistic), but, frankly, it doesn’t matter. Identical twins, particularly when raised together, are extremely similar since they share the same DNA as well as many of the same formative experiences, so it may seem like it would matter, but this is about idealization. This is about their mother idealizing the son she couldn’t have.
I firmly believe that a big part of why their mother hates Touma is that he’s autistic. But they were so young when she gave up Souma that she couldn’t have known then that Touma was different. It’s a case of her idealizing the unknown. At the time, they could only take care of one more child, but she gave birth to twins but she still wanted one and so they had to choose one to give up for adoption, and now, years later, she looks at Touma, who’s different from other children—and from the neurotypical Ryouma—and causes her so much trouble because she doesn’t know how (nor does she want) to deal with him, and thinks, “Ah, things would be different if only I’d kept Souma instead. I wish I had given up Touma back then.” It could be that Souma’s also autistic, and he ended up in a supportive household and he’s more well-adjusted than Touma because he’s actually getting the help and support he needs, and if she met him now it would only reaffirm her wish that she’d kept him instead. But if she had, then it would be the same thing with him, and now she’d be thinking, “Ah, things would be different if only I’d kept Touma instead. I wish I had given up Souma back then.” Because when you get down to it, it’s not really that she wants Souma, it’s that she doesn’t want an autistic child.
But ah, yes, I did say that him being autistic was only “a big part” of why she hates him, not all of it. That’s because what she really wants is a second Ryouma, and Touma’s autism is the most obvious difference between them, the biggest way Touma doesn’t live up to her ideal image of him. If he weren’t, or if Souma isn’t and she’d kept him like she thinks she wishes, I don’t know that it would be “better” per se, but the abuse would look a little different. With how much she’s always comparing him to Ryouma, Souma’s situation would be like Tsubasa’s with his father and older brothers. All three brothers are good at soccer, but since his brothers did it first, Tsubasa being as good as them isn’t good enough for their father. In the same vein, Ryouma is the favored child, and Touma/Souma is living in his shadow, so nothing he does is never going to be good enough for their mother (autistic or not). Souma might not be the autistic child of a parent who views any sign of neurodivergence as undesirable and something to be punished—even as something that he’s doing on purpose specifically to spite her—but he’d still have to deal with never being seen as good enough by a parent who has a specific image of who she wants her child to be and won’t let him be anything else.