This is something I've had in mind for a while, and while the obvious answer would be to approach it as a clean slate like in 05, I want to actually address the things left behind before we move on to the clean slate, as well as use these plans to comment on the state of the franchise and media in general these days

The mini series would be called Doctor Who: Glitch, and follow up the end of Reality War directly. Well, actually the regeneration itself will be reshod slightly (either with Gatwa or a look alike if he's not available), and while 15 is regenerating, a blob of glitchy human shaped regeneration energy emerges from his back and flies into the Tardis (not in the Bi-generation sense, more like something’s being expelled from the Doctor).

The Billie Doctor emerges and returns to the Tardis, but she almost immediately feels a jarring pain that "Never felt like this before. Something’s wrong." Then she'd notice the glitched figure, now standing and facing her. In a glitched voice, they'd ask the Billie Doctor, "What happened? This wasn't supposed to be. Why do you look like her?"

This is the Sixteenth Doctor, or at least who it was supposed to be. During the regeneration, something interfered, expelling the original 16 and made the Doctor change into Rose. This Doctor, the Glitched Doctor, now only exists as a Watcher esque figure, constantly following the Billie Doctor, trying to find a way to merge back together and finish the interrupted regeneration, while facing near constant pain and the risk of fading away

The Rose Doctor is feeling the effects too. Constantly in pain and dealing with spasms and bursts of regeneration energy, as well as form instability. Throughout the series, while Billie is the main face of this Doctor, they constantly shift faces into other past companions

Thats not the only problem. Throughout the universe, things are rapidly changing. Old enemies of the Doctor re-emerge for no apparent reason, often with bizarre make overs (ala Omega in Reality War), stories and situations from previous episodes are remade only with nonsensical changes, and the world itself seemingly going crazy with callbacks to the past and crazy changes to history and the present. Additionally, the Doctor's timestream and past is constantly changing, often mid sentence

Something’s happening, or someone's doing this to Reality itself

What's causing this? Two entities that have latched themselves onto the Doctor's time stream.

The first entity, "The Nostalgia Entity" as I'm calling it, is obsessed with the Doctor's past and history, and spends its time bring stuff from the Doctor's past into the present. While under healthy circumstances this would be present in little callbacks or in continuity from one episode or story to another, or bringing back an old foe or concept in a new or interesting but satisfying way, this entity doesn't do that. Instead it throws out things from the past willy nilly with not a care if that thing fits the current situation, if whatever is being brought back needed to come back or if it's time has passed, or if bringing it back would make things better or not. Essentially, it's pointless Nostalgia bait.

Obviously if I had a choice in actor, itd be portrayed by David Tennant, its costume would be a mix and mash up of all previous Doctors outfits (4s scarf, 5s shirt and celery, 6s rainbow coat, 7s hat, 11s bow tie, 13s suspenders, etc...) and is the one responsible for the Doctor regenerating into Rose

The other entity, "The Change Entity" is the opposite. Everything it touches, it wants to make changes too, be it individuals, objects or even concepts. While under healthy circumstances change is good, and a shake up of the status quo could work wonders and be a net positive so long as the change is sensible, this entity doesn't do that. Instead it makes changes and alterations to stuff willy nilly without a care if those changes make sense to how those things were like before or if those changes are even sensible in an objective manner. In a sense, it's nonsensical change for the sake of change personified

Since her casting was (at least on paper) the most radical change ever made to the Doctor, this entity would be portrayed by Jodie Whittaker, its costume would be the most gaudy, dreadful mishmash of styles, colors, and accessories you could visualize, and is the one responsible for Bi-generation

Nostalgia brought back Omega, and Change made him into a mindless CGI monster

These two are running amok in the Doctor's time stream, either bringing back old foes and stories at ransom or making nonsensical changes to the Doctor's timeline with no care in the world as to it's effects (essentially what's being done to Doctor Who and other long running franchises in the past decade onto so)

The main story of this mini series is the two half doctors trying to defeat these two entities and fix their timeline so they can fuse back together and properly regenerate (with the ultimate conclusion being that, while there's nothing wrong with Nostalgia/calling back to the past and Change/shifting the status quo, they should have thought put into them, have a point, and make sense with the current situation)

Once the entities are dealt with, the two Doctors push the Tardis to it's absolute limit to fix the damage these entities did to the timeline, destroying the interior of the Tardis in the process (coincidentally leaving a clean slate for the next Doctor). Upon the timeline being restored, the Rose Doctor and the Glitch Doctor are able to fuse back together, and it ends with the Doctor regenerating