Here’s an idea:

The Jedi are only an informal order spread across the galaxy. The Knights directly serve the Republic, and can be called on in times of crisis to protect the galaxy, but mostly they are protectors of the individual planets they call home. They are allowed to marry and have children, although their children will not often be strong in the Force. The Skywalkers are outliers in this regard.

The Jedi Masters are entirely separate from the Knights, and are primarily teachers and soothsayers, more like eccentric local wizards than proud warriors. They are often pacifists.

A potential narrative for the prequels would be that Obi-wan was taught by Yoda (who is not the leader of the Jedi Order) on Dagobah, but doesn’t speak much of his master to Anakin. Instead, he decides to teach Anakin on his own and bypass Yoda entirely.

During the Clone crisis, the Senate convenes the Jedi Knights and any Masters who are willing to fight. They get dragged into a long conflict with no end in sight, and during this time Anakin secretly becomes Vader and begins killing the Knights. If there is a dangerous Jedi Master in hiding, Anakin will break their former student and learn of the master’s location. In this way, over the course of some years, he is able to hunt down and eliminate almost all of the Jedi that are of any real threat. The final student is Obi-wan, and Anakin is intent on learning of Yoda’s location so that he can become immortal.

For you see, Yoda had another living student, one who was an old man by the time of the Clone crisis. Anakin tracked him down and attempted to kill him, but as he delivered his killing stroke the man turned invisible, and Anakin heard a mocking laughter in his head. Desperate to learn the secret to evading death, Anakin tracks down Obi-wan, who tells him that contained in his Jedi training was the secret to immortality and peace, but Anakin had become too fallen to recognize it anymore.