On a practical level, Obi-Wan did not know that Anakin had survived simply because he was isolated on Tatooine. Although Obi-Wan did not see Anakin die after their battle on Mustafar in Star Wars: Revenge of the Sith, he reasonably could have assumed that Anakin would die from his injuries.
Obi-Wan Kenobi always blamed himself for Anakin's fate. "Anakin was a good friend," he explained to Luke in Return of the Jedi, manifesting as a Force ghost. "I took it upon myself to train him as a Jedi. I thought that I could instruct him just as well as Yoda.
Obi-Wan's guilt over failing Anakin is what drives his character to watch over Luke Skywalker on Tatooine. In a way, keeping Luke safe and then teaching him the ways of the Force is Obi-Wan's way of getting redemption. He feels terrible for failing Anakin, because he believes he robbed Luke from having a father figure.
So, at that moment on Mustafar, Obi-Wan should have finished Anakin, but he didn't have the courage to do it because ironically he had an attachment to Anakin. He couldn't even do what would be the best solution (take Anakin with him and try to bring him to the Light) or what the Order dictated (destroy the Sith).
In the material around the film from the Legends timeline, it's established that by the end of Star Wars: Episode III - Revenge of the Sith, Kenobi was one of the characters who knew Anakin's Sith name was Darth Vader. However, what he didn't know was that he was still alive after Mustafar.
Obi-Wan Kenobi 2022 Final Scene | You didn't kill Anakin Skywalker, I did...
Did Obi-Wan regret not killing Anakin?
David Porter provides some great philosophical context to why Obi-Wan would not regret leaving Anakin alive, as it was obviously “the will of the Force” that Obi-Wan be unable to finish him off, and “the will of the Force” that Anakin live on to kill Sidious himself in the future.
He couldn't bring himself to kill Darth Vader, however, because he continues to associate him with the Anakin he trained as a boy. This is also the exact reason why Obi-Wan didn't kill Anakin on Mustafar despite the opportunity a decade earlier in Star Wars: Episode III - Revenge of the Sith.
Secondly, based on their last encounter on Mustafar, Anakin was obviously too far gone to the Dark side as he had just gone on a killing rampage in the Jedi temple. Obi-Wan thought that he's far beyond redemption; in hindsight, not really understanding what drove Anakin to the Sith didn't help the situation.
Thanks to that scene, there are now two possible explanations for the sudden jump in Obi-Wan's physical age: it was a result of the Dark Side of the Force being used against him, or it was a result of the burns he suffered.
Kenobi bested Anakin, severing his limbs, and leaving him to die, burning on the shores of a lava river. Darth Sidious recovered Anakin's broken body and returned with him to Coruscant. Medical droids rebuilt Anakin with cybernetic parts, encasing him in dark armor to complete his transformation into Darth Vader.
The canonical comic Star Wars: Darth Vader #7 confirms the younglings' deaths caused Anakin grief, self-loathing, hatred and pain, fueling his descent even further into the dark side.
Although the decision to turn to the Dark Side was Anakin's alone, the choice did not come from thin air. His natural prone to impulsivity and emotion without the support systems he needed in place made it easier for Anakin to stumble down a path of darkness.
Anakin Hated Obi-Wan Because of an Imagined Relationship With Padme. Although Padme and Obi-Wan's affair couldn't have been further from the truth, Anakin apparently built up a scenario in his mind, which was only heightened by the Jedi Council's obfuscation in other areas.
After defeating Darth Vader in the Obi-Wan Kenobi finale, Obi-Wan broke down and began tearing up when he saw Anakin's scars. It was the first time he had seen Anakin's face since leaving him to burn on Mustafar, and so he apologized for everything that had happened.
After his redemption, after bringing back balance to the force, after the return of the Jedi, Anakin would have definitely held a bit of remorse, not to forget, it was Obi-wan who taught Anakin how to become a force ghost, to stray oneself from the cosmic force and assume identity with the living force.
Many are often shocked to find that Obi-Wan was only 57 years old when he died fighting Darth Vader in A New Hope. For many, the issue of Obi-Wan's age is a plot hole, as he was initially seen as this old solitary man, but Star Wars made him younger than he looked in the original trilogy.
Darth Vader, the man that was Anakin Skywalker until his early twenties, is now a 32-year-old Sith Lord in his evil prime. By contrast, the once-optimistic Obi-Wan Kenobi is weaker: a 48-year-old former Jedi trying to part ways not only with his past but with The Force itself.
As the heat began to consume Anakin, a grief-stricken Obi-Wan turned away, unable to watch his former Padawan and friend die. But Anakin lived. Rescued by Darth Sidious, he was encased in black armor and became known as Darth Vader, the Empire's brutal enforcer.
Palpatine may still have eventually traded Dooku in for a newer apprentice, but nothing would have hindered his rise to power. Had Qui-Gon trained Anakin and kept him far from Palpatine, Anakin might have eventually died in the Clone Wars and been completely unable to fulfill any Chosen One prophecies.
Obi-Wan knew that even if he defeated Darth Vader, he could never have fled the Death Star, so he accepted his fate and let Vader's lightsaber strike him down.
Vader responded “I am not your failure, Obi-Wan. You didn't kill Anakin Skywalker. I did.” This allows Obi-Wan to finally accept that Anakin is truly gone and that there was nothing he could have realistically done to save him.
For years, Vader hated Obi-Wan, having been struck down by his mentor and left for dead while also believing the Jedi had worked to turn his true love Padmé against him.
