Learn Russian: Он только что ушёл.

While как только means "as soon as" and connects two events in a complex sentence, только что is a standalone fixed phrase meaning "just" or "just now". It is used to show that an action was completed a very short time ago.

Why does Russian use the past tense ушёл when the English translation says "has just left"?

English uses the present perfect ("has left") for recent events with present relevance, but Russian uses the past tense of a perfective verb. The perfective aspect of ушёл already does the job of showing that the action is completely finished and the result matters right now (he is no longer here).

Could we use a different verb of motion here, like пошёл or вышел?

You could, but the meaning changes. Ушёл emphasizes that he has permanently departed or left the location. Вышел implies he just stepped out (like out of a specific room, perhaps temporarily), and пошёл means he just set off on his journey.

Can I put words between только and что?

No. When used to mean "just now", только что acts as a single, indivisible phrase. You cannot separate them with other words.