I know the leak has been pretty accurate so far, but for some reason, Tennant's new costume and screwdriver make me question the idea that 13 turns into Tennant.

That it's almost but not quite the same costume made me figure that soon after realizing he has Tennant's face again, he just tries to put on whatever in his vicinity will most approximate the costume like the one that he wore when he had Tennant's face. I just think that he'll have to be wearing that before he runs into Donna again because if he knew that he'd be running into Donna, then I don't think that he'd wanna try & make it clear that he looks exactly like the Doctor that she'd recognize, given that doing so would risk triggering a DoctorDonna meltdown. And as for the screwdriver, I figured 13's is broken for whatever reason & so the new Tennant Doctor either makes or has the TARDIS give him a new screwdriver; after all, both 11 & 12's just popped a new one out of the console at different points, & 12 had all of them on his desk.

I'm leaning towards parallel world or dream.

To be honest, I think that the degeneration leak is true... to a point, because RTD is a notorious troll of the fandom, one who's even admitted to having had fake leaks planted online in the past, so I'm personally thinking that the leak is wrong about 2 things: that David & Catherine are back for all 3 of the specials, & that all 3 of the stories are linked by the new Tennant Doctor working out why he got his old face back & why he ran into Donna again after all these years. Instead, I think that David is only coming back for the final scene of the Centenary & the 1st of the 3 anniversary specials. The 1st of those 3 specials, the one that's being filmed right now & being directed by Rachel Talalay, will be the one in which David & Catherine are back & in which the new Tennant Doctor tries to work out why he got his old face back & ran into Donna again.

Now, my theory diverges from the leak in a pretty significant fashion here due to Chibnall's final episode-to-be, the Centenary special. Given that it looks like it's gonna exclusively be a nostalgic love-fest for Classic Who as the reflection upon the historical side of Doctor Who for the BBC's 100th, I won't be surprised if, in retrospect, its events are also the driving factor/first half of the events that take place in the anniversary specials in order to render the plot thereof unique beyond the usual running into multiple old Doctors at some forgotten point in their lives. So, maybe something arising from the Centenary plot involving Tegan & Ace will happen to 13 that causes her to begin suffering from a Time Lord-specific degenerative ailment, hence 5, 6, & 7's rumored Centenary appearances: they'll be the first incarnations to pop-up (Colin's cameo may be quick one, but you'll get your 5/Tegan & 7/Ace "reunions"), with the final shot being 10.

From there, I predict that the new Tennant Doctor will work out over the course of the 1st anniversary special why he ran into Donna again &, having dealt with the Nobles, will then try to regenerate again, only for it to be another degeneration, producing a new Matt Smith Doctor. This cycle will repeat itself in the 2nd special, just replace the Nobles with the Ponds, & the 2nd special will end with the new Smith Doctor trying to regenerate again, only to be Peter Capaldi. The cycle repeats again not with a companion of his but with Susan (given the classic aspect of the leak, & I think it's the Capaldi Doctor that gets to "come back" because she was most-referenced during his era, plus maybe this is the good-enough script that actually managed to get Capaldi involved after saying that he wouldn't wanna be), & the special ends with the Capaldi Doctor in his TARDIS after having worked out why he kept getting his old faces back, curing the problem, & quickly morphing back into Jodie (thereby ensuring that no regenerations were wasted in the making of these specials since the current Doctor was still 13 all along, just 13 who was struggling from the degenerative ailment) before ably regenerating into Ncuti's 14.

So, basically, the Centenary is the old-school special that pays tribute to Classic Who (as a part of the BBC's tribute to its 100th birthday), & the anniversary specials are the specials that celebrate the show's modern eras, but they'll both intertwine to salute the show as a whole, & in such a fashion that ensures nobody has to worry about 13 &/or regenerations being wasted.