Although we never see him teach anyone else, it is established that Jedi Masters do teach larger classes at the Jedi Temple, as illustrated by Yoda in Episode 2. Since Obi-wan is a master, it is logical to assume that he has such a duty as well which he could have been doing briefly right before Episode 3:
Episode III
Revenge of the Sith
As the Clone Wars ravage the galaxy, Anakin has returned home from his long campaign to Coruscant to become a Jedi Master.
Now without an apprentice, Master Obi-wan has become a teacher at the Jedi Temple, but he is eager to return to battle and end the war.
So when the Droid Leader General Grievous attacks Coruscant and captures the Chancellor, the two Jedi gladly embark on one last mission…
Since he’s teaching a large class of pupils and doesn’t care for the job, it’s somewhat understandable that we don’t see or hear anything about this in the movie proper - it’s a largely unwanted and uninteresting duty that he’s happy to ignore if he can. If he had a second apprentice on the other hand, that would need to be established in at least one scene.
In this edit Anakin is much more of a hero, since he wouldn’t slaughter Sand People or be suspicious of the Jedi. With these scenes removed, I think that he would play as a tortured yet ultimately heroic figure, and since there are no scenes of what happens to Anakin in the Jedi Temple, in the moment the overriding assumption would be that Anakin was killed through some means that is intended to be secret. Then in ANH, Obi-wan reveals that it was in fact one of his pupils in the Jedi Temple who betrayed and murdered Anakin, which makes complete sense in setting up a sequel where they need a secondary villain with a relationship to the hero. His apparent abandonment of these pupils in the beginning of Episode 3 has come back to haunt him, it seems. I think it’s as reasonable an assumption as the idea that Anakin fell to the dark side and immediately turned on the Jedi who practically raised him.