I know a lot of people were sad that Yaz just walked away and there was no kiss etc but I think it was fundamentally a good ending for them and for Yaz.
The Doctor has learnt from experience that they will keep on going in whatever form (the timeless child story has made that even more underlined) but unfortunately, their human companions cannot. In terms of romance, 10 learnt the hard way with Rose. 11 learnt what it was like to loose family in Amy and Rory and 12 lost a soul mate in Clara. In twelves case he lost her despite how desperately he tried to cling onto her, going to the absolute extremes.
13 has shown that she has learnt those lessons. She has clearly learnt not to cling onto those relationships, as demonstrated by the exits of Ryan, Graham and Dan. In Yaz's case, she had fallen for her companion and knows the feelings were reciprocated. In fact, she even subtly admitted to those feelings in Legends of the Sea Devils. However, having learnt the lessons of the past, she asked Yaz to go on as they were and not make that step into a romantic relationship.
Yaz could do nothing but agree to this, but it was clear in the Legend of the Sea Devils that she still didn't 100% understand why. This is were Yaz meeting Ace and Tegen was important to what was to come. The Doctor evolves and regenerates, and perhaps more quickly than Yaz had realised. In Ace and Tegan you have two former companions, with an age difference but not a vast one, who clearly know the Doctor as different regenerations. Having Ace there highlights it quicker because she of course refers to the Doctor as 'Professor'. Yaz already knows the Doctor was a Scotsman in the last regeneration.
The key line was when Yaz said 'where is my Doctor?'. Not THE Doctor. Not THE REAL DOCTOR. My Doctor. Going through a regeneration with the Doctor is hard enough for a companion even when they are just the Doctor's friend. Yaz doesn't feel like that about the Doctor, she is in love with her. She is in love with her mannerisms and her personality. No doubt, she is also physically attracted to her too. It's not just as simple as getting used to a new character to go off galavanting with. Yaz tried to save the woman she loved but despite everything she failed. She saved the Doctor, but not her Doctor. It was poignant that Yaz, having seen regeneration energy before (and now a forced regeneration), was the first to realise what was going on. Instead of panic or histrionics there was just a sad realisation that it was over.
The Doctor knows this and feels for Yaz in return. Imagine regenerating and looking at the person you have come to love, only for them to look back at you like you are a stranger? The Doctor knows that everything has its time and place. Yaz has been with her since she first regenerated until her final moments. She is Yaz's Doctor, but Yaz has been her consistent companion. It made sense for her to go onto her next journey alone and it made sense for Yaz to step away and remember her as 13, but in the knowledge that the Doctor is safe and will go on. The Doctor singled out the fact that she had loved her time with Yaz in their final quite moments together. In the end, it was all very mature from both of them.
Now, if you are a Yaz fan, take heart. There is rumour abound that RTD would like to make an extended Doctor Who world (mini marvel style). If this was to happen, expect to see a revival of Torchwood and its very feasible that an Agents of Sheild style UNIT series will be considered. What did Kate say in the support group? She might try and recruit them! It's very possible that we may see Yaz again and other companions. We may even see an old Doctor or two...
