Out of universe answer - Russell T Davis was very aware of potential concerns around cross-dressing or anything that could be seen as the 14th Doctor cross-dressing. So he made a deliberate choice that only the 13th Doctor would wear her clothes. (although this misses the precedent set by the forced regeneration into The Master"
In universe, on the fly I would say, an abundance of energy following either the destruction of much of the universe in the Flux or following the machinations in the Flux by and The Master's manipulations in her regeneration and the consequent fix meant that the current clothes burnt up and new ones were able to be manipulated directly from the latent energy, converting energy into matter, by redirection of the regeneration energy.
They have already established that it was a subconscious regeneration into a previous face to send a message to slow down, this could have subconsciously extended to the clothing if there was enough latent energy.
Second doctor's outfit simply changes, Third Doctor could have regenerated those clothes that feels somewhat implied to me, a recent Big Finish story had a thing called Degeneration and outfits changing each time
Also Doctor Who is a weird show to be complaining about continuity.
The Doctor is a human from the future wait no a Time Lord Fugitive or maybe he is the founder of Time Lord Society (The Other/Seventh Doctor), Eight fought in the Time War never mind that was John Hurt but here is a new story about Eight ending the Time War after that retcon, The Doctor has thirteen lives and the Valeyard happens but then who are the Morbius faces and they are the founder of Time Lord society again with hundreds of lives but in a contradictory way to him working with Rassilon
I also agree it is a unique regeneration, in the modern era picking out the clothes is part of establishing a new identity but 14 is someone with other things to figure out, why this Doctor is back. So the clothes come with that. One could also say he stopped letting regeneration change his clothes once he learnt he cared about his presentation as an identity forming thing as opposed to letting Regeneration handle that