A text message is not automatically admissible as evidence. Even if admitted, he could deny sending the messages. It would then be up to the prosecution to prove beyond reasonable doubt that he sent the messages, rather than someone with access to his phone. Even if it is accepted he sent the messages, it is relatively easy for the defence to throw doubt on them as a true admission of guilt. It is nowhere near as good as a confession in a statement made under caution.
If he was convicted of assaulting his sister, he would almost certainly get a community order in the circumstances described.
Whilst Letby's text messages were put into evidence against her, they did not include a confession.
Since some people are bringing religion into this, I would point out that, on the information we have, there is no reason to believe it had any bearing on the CPS decision. If they cannot prove that the punch caused the girl's death, they would not prosecute regardless of the religion, race, age or sex of the alleged perpetrator.