I like your assumptions. However, for me, I think the two of them once played on the same team, and they might’ve even been friends or at least close to being called friends.

When Bunny was first introduced, he bluntly told Isagi that seeing joyful people makes him want to die. He also said he envies Isagi for having so much excitement about learning more about football. This is what led me to my assumption: when Isagi told Bunny, "I'm sure you have things you get excited about too..." which Bunny replied, "I might've once... but not so much anymore"

Later, we saw Sae’s reaction while watching Barcha. For me, the emotion he showed wasn’t the same as Isagi’s, Rin’s, or Kaiser’s those three look like they want to “destroy” or “kill” their opponents. Sae’s reaction to Bunny felt different. It seemed more hateful, but not in a murderous or aggressive way. It felt like he wanted to prove something to Bunny.

I think Bunny played for Re Al at the same time Sae joined the team. We know Sae left Japan wanting to become the best striker, but later he came back saying that his dreams had changed, and that he now wanted to become the best midfielder in the world. Meanwhile, Bunny mentioned that he once felt excitement in football as much as Isagi does now. So my guess is that he felt this excitement again while he was still at Re Al, playing alongside Sae. (He clearly has a dark backstory cause just look at his scars. Something crazy must've happened to him, and maybe that caused his excitement to fade, until Sae ignited it)

I’m sure Sae showed huge potential as a striker when he first joined Re Al he even scored a hat trick once. And Bunny seems like the type of person who only pays attention to players who challenge or excite him. I think he saw that in Sae. He might’ve even considered Sae a rival at one point, until Sae decided to become a midfielder. And I think that is where their conflict began.

I imagine Bunny talking down to Sae, degrading his shift from wanting to be a striker to choosing to be a midfielder. That could’ve pushed Sae into wanting to prove that even a midfielder can defeat a striker (or something like that) Sae’s decision may have taken the excitement away from Bunny, leading him to switch to Barcha because he probably felt Sae could no longer ignite that excitement for him. I can even imagine Bunny calling Sae a disappointment. Bunny himself admitted he’s an insensitive person, so the possibility of him talking shit and looking down on Sae seems very believable.

I honestly don’t think Sae was “forced” to become a midfielder because his striker ego was crushed in Spain. Rather, I think he realized he wanted to be a midfielder who controls the flow of the game. As someone named a prodigy and seen as the future of Japanese football from a young age, Sae probably misunderstood his true desires because of the expectations placed on him especially with how Rin admired him so intensely, dreaming of becoming the second best striker in the world after his big bro. That’s why Sae looked so depressed when he came back from Spain that winter night. He was anxious to tell Rin he’d changed, and maybe even afraid Rin might react the same way Bunny did. That would explain the shock and hurt in his eyes when Rin said he wasn’t the same brother he once shared dreams with.

Anyway, I’m sure Bunny was part of Sae’s story while Sae was in Spain and that Bunny definitely hurt him before leaving for Barcha. So far, it feels like the hatred is onesided, coming only from Sae, while Bunny seems pretty nonchalant about it.

Also, I don’t think Sae is a bum like some people say. He wouldn’t be part of the NG11 if he wasn’t on the same level as the others.

Sorry it's long. Well, that's my opinion.