Now, granted, I am totally talking about these ideas as someone who hasn’t seen the season 7 finale since it aired. But I’ve enjoyed the idea, something that has been given a bit of credence in Gatwa’s first season, of the Great Intelligence being the Shalka Doctor because of how he entered the Doctor’s timestream. Somehow he kind of becomes a secret incarnation. How that functionally works I would have to go back and rewatch that episode and see if I can string it together. I also have not seen Trial of a Timelord yet, so this is going off what I understand of a certain character from it. I am willing to be informed on stuff I may not know.
But what do you all think of the idea of him being the Valeyard as well, perhaps all three the same? Great Intelligence > Shalka Doctor > Valeyard. It would put the Valeyard at being someone near the end of the Doctor’s original regeneration cycle and also be someone who is a “darker version of the Doctor” or who would want to destroy him and has gone back in in his timestream to do so.