Curate, connect, and discover
Reverse robins is an interesting concept that's being do underutilised it hurts. Just because the order of them being adopted and their ages are reversed doesn't mean that major events are set in stone; just because Tim was adopted second doesn't mean he would've died, or that he would become the red hood. Jason died because he felt like being bruce's son hinged on him being robin, and so went to find his mother that sold him to the joker. Tim doesn't come from Jason's background, he doesn't NEED to be told he's loved to get it, and he was still bruce's robin when his parents were still alive so it doesn't make sense giving him the secret bio mom thing.
Also Tim wouldn't become the red hood and set up shop in crime alley because why the fuck would he? what connection does he have to that place? He's the most practical robin, so if he was to have a red hood esque character, he would never even reveal himself to the public, just operate behind the scenes. Jason's dramatics are a call for attention from bruce. That's his whole thing, wanting bruce to confirm his love and validation. Giving all of that to Tim is a disservice to both characters.