Trinity and Morpheus look different in The Matrix Resurrections' opening sequence, and the reason has to do with Neo's Matrix modal. More than 18 years after The Matrix Revolutions - 60 years in-universe - audiences were brought back to the Matrix to once again follow Neo and other iconic Matrix characters, except that not everything looked like it used to. Neo once again has to dive into a journey of self-discovery, and that is the key not only to the plot of the film, but also to explaining why some characters and events are different in The Matrix Resurrections.
After The Matrix Revolutions' ending saw Neo achieving a truce between humans and machines, it would seem that peace would finally be upon both the simulation and the real world. However, now that humans could choose to leave the Matrix and walk away freely, the machines were faced with a power outage issue. That was the cause of a machine civil war, a scenario that prompted The Analyst and its faction to rise to power with a plan for a new version of the Matrix. In the center of that plan were Neo and Trinity, who, when placed together inside the Matrix under specific circumstances, were capable of generating much more electricity than other humans.
Neo was now back to being enslaved inside the Matrix, but The One's subconscious was powerful enough to start creating an escape plan. That is how Neo's Matrix modal - a sandbox program in which new "characters" and events could be run - came to be. Neo could not access his memories, but he was still able to subconsciously run a simulation that resembled his story in the first Matrix movie. That is why The Matrix Resurrections opens with an almost one-on-one reenact of The Matrix's opening sequence. However, given how not even Neo himself was sure of what his memories meant, that subconscious modal simulation was not all faithful to how everything happened in The Matrix – hence why Trinity looked different, why Smith and Morpheus were played by the same program, and why Trinity's fight against the agents did not go as it did in The Matrix.
Just like in The Matrix, Neo was once again questioning his reality due to the constant feeling of something being off. That same sensation was carried onto his Matrix modal simulation, and even Bugs could realize that something was off. The story of The One and how Neo and Trinity had ended the war remained famous through 60 years — and watching that slightly different modal was how Bugs and her team were sure that Neo was asking for help. Yahya Abdul-Mateen II's Morpheus, who was there to guide Neo out of the Matrix, was, therefore, the personification of Neo's cry for help.
The Matrix Resurrections' plot is meta on many different levels, but the rehash of The Matrix's opening sequence with a different Trinity and the new Morpheus actually works for the story. In a way, Neo directed a flawed remake of the first Matrix film inside his modal. Distinguishing between what is real or not and the feeling of something being off were central themes of The Matrix and its sequels, and those could not be absent from The Matrix Resurrections.