My takeaways from this episode:

1. The Doctor mentions that this is the first time he's had "this" black body, and yet, later on in the episode, he displays undeniable proof that he remembers an experience from when he had a certain other black body (i'll get into that in another point.)
2. When you imagine what the result would be if you bring in a black Nigerian man to write for the first mainline black Doctor for an episode set in Nigeria, that opening scene in the TARDIS and the sense of community The Doctor has found there is exactly what you're expecting, and it's one of my favourite moments right off the bat.
3. JO F*CKING MARTIN!!!! Cameo aside, if The Fifteenth Doctor definitely remembers an adventure he had as The Fugitive Doctor, even offering up their account, are we to take it that in between the final episode of Flux and this one, The Doctor just dug out the fob watch from the depths of the TARDIS and fully reunited with their Timeless Child self off-screen? If so, i kinda f*ck with it.
4. So, if, bottom line, The Doctor definitely remembers being The Fugitive Doctor, then why did he say this is the first time he's been black? Answer: he didn't, he said this is the first time he's had "this" black body. So, if you read between the lines, are we to take it that the Timeless Child reused bodies from time to time? What if The Timeless Child has previously looked like Paul McGann or William Hartnell, Peter Capaldi, Jodie Whittaker, etc.? What if that's the gift of The Timeless Child's species? Time Lords can't reuse faces, but The Timeless Child can with relative ease. What if David Tennant coming back was one such example of the Timeless Child shining through the Time Lord biology rewrite, except The Doctor clocked it this time because it was a face reused from after the mind wipe? What if being David Tennant again motivated The Fifteenth Doctor to find out more about his Timeless Child self and what they could do?

OK, i'm kind of going a bit too hard into Fan Theory territory, but still, outside of the implications to the wider Doctor Who lore, this episode works really well on it's own. I had a really fun time watching it.