Sonic is the true ultimate lifeform. This is not a "theory" and you don't need murals from other games to make sense of it (as interesting as that can be), it's a major and self-contained plot point within Sonic Adventure 2 itself.
Shadow was created to be the ultimate lifeform. But everything went wrong and Shadow woke up in a time where he doesn't belong. And there he meets Sonic, someone who looks just like him but isn't haunted by the memories of his past. Surely this is just a coincidence, right?
From our perspective as out-of-universe observers who know Shadow and the "ultimate lifeform" concept were invented a whole decade after Sonic's first game, we know it's obviously Sonic who came first, but the game is seemingly telling us this cooler and darker Sonic "actually came first". Of course Sonic does not know Shadow's backstory yet on their first meeting, so he has the same perspective we do. Who is this faker that looks like Sonic's shadow? He introduces himself as the "ultimate lifeform" and using the Chaos Emerald he just stole shows his unique technique that no one else can perform: Chaos Control.
During most of the game, Sonic and Shadow confront one another and Shadow is increasingly surprised by Sonic's abilities. Shadow's tragedy 50 years in the past is later paralleled: Eggman is pointing a gun to Amy's head and Sonic rushes to rescue her. Sonic brings the fake Chaos Emerald that Tails created to trick Eggman, but Eggman isn't fooled so easily and finally manages to kill Sonic by making him explode in space, while Shadow watches. Turns out Sonic was just a regular hedgehog after all. Or is he? Shadow is surprised once again. Sonic managed to use Chaos Control, Shadow's unique technique, using an inferior artificial replica of a Chaos Emerald. This comes right around the time Rouge starts questioning Shadow's identity. So Shadow confronts Sonic one last time and finally asks him who he is. But unlike Shadow, Sonic does not care for his identity or purpose, as far as Sonic is concerned he's just someone who enjoys having fun.
Shadow was created by Professor Gerald as part of Project Shadow. This is a part of the storytelling that is not directly mentioned in the story or script but is rather communicated through the enemy design and the environment. The creations that came from Project Shadow are based on things that were observed. Similarly to the fake Chaos Emerald created by Tails, the creations of Project Shadow are replicas of ancient technology, ancient beings, and ancient mystical stones. Enemies like Artificial Chaos, objects like the Chaos Drives, and the replica of the Master Emerald shrine found deep within the ARK, were all created to research immortality as part of Project Shadow with Shadow himself as the final product of the project. But what is Shadow himself a replica of? There can't be a shadow for something that doesn't exist. But it turns out that's what the ultimate lifeform needs to look like. Perhaps it was prophecized in ancient cultures. Even if he apparently came later, Sonic is nature's own ultimate lifeform.
Shadow was artificially created first, to fulfill a role. Sonic appeared naturally in the world, and just so happens to fulfill that role. Natural versus artificial. Justice versus evil. Yin versus Yang. Light versus shadow. Creation versus destruction. Truth versus lie. Original versus fake. Hero versus Dark. This story of rivalries and opposites ends with the two sides working together. Sonic and Shadow use Chaos Control, the meeting of two opposites, to save the Earth.
Sonic may be the true ultimate lifeform, but he never cared for that title. So who is Shadow? He is who he is. And who is Sonic? He's Sonic the Hedgehog!