Although Jesse has been through several different forms of hell by the time El Camino starts, he's still quite young, when you look at the broad picture. "Felina" — which El Camino takes place immediately after — is set on Walt's birthday, which is known to be September 7. Because Walt is turning 52, we also know that the finale is taking place in 2010. Jesse's age was first mentioned by Gus's doctor in the episode "Crawl Space," and Jesse's birthdate is established as September 24, 1984, which means that during the events of both "Felina" and El Camino, he should be 25 years old. It's entirely possible that he turned 26 somewhere in the middle of the events of El Camino, but it's not mentioned, if so.
As for why Aaron Paul looks older than that: El Camino was released in 2019, several years after the end of Breaking Bad. That means that, although Aaron Paul was playing a 25-year-old (or 26-year-old) in the movie, by the time it was actually filmed, he was roughly 39 years old.
The thrust of the movie involves Jesse's attempt to escape from Albuquerque and start over in Alaska. By the end of the movie, he's gotten the happy ending that he's been working for. Given his relative youth when the movie ends, it seems that Jesse still has plenty of time to find some happiness, even if the past few years of his life were so horrible.
