A very crucial scene in Return of the Jedi established that Obi-Wan Kenobi (a Force ghost by that point) blames himself for Anakin's fall to the dark side. He explained to Luke, “I took it upon myself to train him as a Jedi.
Obi-Wan Kenobi blamed himself for Anakin Skywalker's fall to the dark side, and for the birth of Darth Vader. Ironically, though, it was not his arrogance that was at fault; rather, it was his own sense of attachment.
“I have failed you, Anakin,” Obi-Wan told Anakin in Revenge of the Sith. And it's the guilt of that — this feeling that he has created a monster — that Obi-Wan has carried ever since.
The 2022 Obi Wan Disney+ series shows us the very moment Obi WAN discovers Anakin (or Darth Vader) is alive and did not die on Mustafar. There's material in that series that specifically points out he did not regret leaving him alive.
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.
First and foremost, Obi-Wan didn't want to have to confront and try to kill Anakin, we see this all the way until their final conflict in their duel where Obi-Wan pleads with Anakin to not make him do what he knows he'll have to do if Anakin tries to attack from the low-ground.
Before he discovered Vader had survived Mustafar, Obi-wan lived with the regret of killing his son, brother and best friend. After, he regretted not killing him and wondered if he had only made things worse by pushing Anakin further into dark side and Palpatine's arms.
Anakin admits to Obi-Wan that he has been arrogant and unappreciative of his training, and apologizes to his master. Obi-Wan assures Anakin that he is proud of him, telling him that he has become a "far greater Jedi than I could ever hope to be."
Now we know why Anakin Skywalker said Obi-Wan was "holding me back!" “I'm really ahead of him.” In Attack of the Clones, Anakin Skywalker makes this casual boast about his master to Padmé Amidala and later, claims “It's all Obi-Wan's fault! He's jealous!
He slays Sidious and returns to Obi-Wan, begging for atonement by execution, only to be met with true forgiveness instead. But just as this fantasy Obi-Wan refuses to strike his former friend down, Vader refuses to turn his back on the dark.
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.
Obi-Wan knew it was only a matter of time. So, he made the difficult decision to use his learnings and become one with the force, rather than let Vader decapitate him.
Arguably, most Star Wars plot points revolve around characters simply not knowing something, very often about their family history. But, on top of all of that, the biggest reason Obi-Wan doesn't know Anakin is alive is that the last time he saw Anakin Skywalker in Revenge of the Sith, Ben literally left him for dead.
It mostly stemmed from Anakin feeling that he was shown disrespect by the Jedi High Council when it wouldn't promote or trust him as much as he believed they should. This condescension is something Anakin often voiced to Padme Amidala, who would oftentimes offer him consolation.
And so, Obi-Wan tells Anakin not to try it, because "he, just like Anakin now, had once been in a position where success requires a massive vertical leap over your opponent and he knew the risk that move entailed," as the Reddit user says.
The short answer is yes, without a doubt, Vader regretted becoming a cybernetic monstrosity. First, there's the constant pain and discomfort from his suit. Worse, however, is the psychological pain. Vader destroyed everything he had ever known for a chance to save Padme.
The added risk Darth Vader takes in allowing children to live in a situation where he could have killed them proves that he regrets killing Younglings and will avoid harming any more children for the rest of his days, though intense intimidation is a dark strategy to avoid repeating his Youngling massacre.
The Third Sister was at the Jedi Temple during Order 66. She either saw Anakin kill her fellow Jedi or saw the recording of his crimes. That's why she has such hatred for Obi-Wan. She was a Padawan who escaped Order 66.
We go for the more simple answer, further considering the details of the question itself. If Anakin didn't go into that chamber as the Jedi confronted Palpatine, then Mace Windu would have defeated Palpatine, killing him. If you remember, Mace had him. He was ready to kill him.
This was addressed in Star Wars: The Clone Wars, teasing that Obi-Wan was at the very least suspicious but chose not to confront Anakin. The animated show also revealed Anakin's jealousy over Padmé, foreshadowing his instability and dependence on her love.
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.
Yes, his entire character since then was a self loathing tragic monster who has little reason to care about anything. Betraying Mace Windu instantly made him regret his act of impulse, Padme's death and rejection of his actions later on made it stick.
Darth Vader hates Obi-Wan, not because he blames him for his fall to the Dark Side, but because he turned Padmé against him and destroyed his body.