Wow, this thread blew up. Thank you to everyone for your input.
To fill in some info gaps, I'm on the east side of Round Rock so it's not the hood but it's not Eanes ISD either. I don't know for sure what the punishment is for the other student other than the principal telling us that our son wouldn't be seeing her around school for a while. I don't know if that means at-home suspension, ISS, or moving to an alternate campus. It's very annoying that the school officials want to speak in riddles since they can't give specifics.
I talked with my son more about it last night. He seems unphased by it. I did hear him over the weekend talking to his friends on discord and he told them he thought he tripped until he overheard the principal telling his grandmother they saw someone push him when they watched the security tapes so I don't think he's BS'ing about knowingly getting pushed. He did mention to my mom yesterday when she picked him up from school that he's going to start holding onto the handrail while going down the stairs just in case.
A side story to this, he's been bugging us for a phone since last year because most of his friends had them. Then when he went back to school this year, one of his teachers took a poll in one of his classes of students who had phones and he said he was one of only a few who didn't. Fast forward to Friday when this happened, the nurse asked him if he could call his parents and when he said he didn't have a phone, she seemed surprised. So when my mom got there to pick him up, the nurse and principal were saying it would be a good idea to get him a phone in case of emergencies. I finally relented and got him one this weekend so he's been on cloud 9 about that. He even said last night in a joking manner he was glad he got pushed because he finally got a phone as a result.
Anyway, we're going to move forward with pressing charges so I'm sure I'll check in with updates once things progress.