Really and honestly, thirteen dying and Yaz knowing she was dead was the kindest way to separate them. Yaz just got a masterclass on regeneration, she Knows there are different doctors and is even heard to place claim on This doctor as her own.
In revolution of the daleks, Yaz calls 13 on her statement that she won't disappear again by telling her that yes. She Would. 13 didn't have an answer because it was entirely correct of a statement.
But thirteen didn't disappear. She died. And Yaz knows that and I know it's semantics, but sometimes that's just what we're left with in life to be frank. So 13 left her, but not because she walked away or wanted to ditch her, not through some painful inconclusive situation like the timeless children where Yaz did not know for sure enough to move on. This was different.
She left because she died.
That is something that will probably be much easier to deal with in the long run for Yaz. Even if she knows there's another regeneration out there, it's not Her regeneration and she made that distinction herself. She will hurt and grieve but she will move on and live as well afterwards with no uncertainty.
And Yaz understands that, too. She knows the doctor is out there, and it's a comfort to her. But not Her doctor. So she bowed out of her own will. A "the king is dead, the king is alive" situation (@ the doctor don't slap me for that analogy).