Honestly thinking of the fallout.
I suspect the Tarkin Doctrine, or something suspiciously similar would still be one of the main doctrines. Partly because Tarkin is one of THE most influential admirals in the Empire, partly other officers ranging from political appointees to gems in the Rough like Maximilian Veers, the big designers in places like Kuat whom are invested due to designing Tarkin Doctrine ships already, Palps having a preference for such methods, and the fact that in a pit of vipers that is military office politics, having the best ship can insulate yourself from some of the dangers somewhat.
But, it is likely departures to standard imperial methods might be accelerated, with Moffs likely to start diverging from the standard, reflecting their own insights and preferences through the equipment and ships they acquire. Which may lead to Thrawn getting the backing of more fighter-focused Moffs, as there needs to be new Imperial designs to truly push their fighter corps above the rest without knife-fighting over the limited pilot poll. Though there may be side efforts to get personal pilot pipelines, which while may not be up to empire standard, would help them field more fighter-craft than the allotted pilots could.
And then, there is the very real possibility for a sort of Constantine Doctrine, where a few Imperials may seek to emulate the Moff, taking cues from his own operations and the points made when tearing into the Tarkin Doctrine. Though with how little we know, it is hard to say what exactly the theoretical doctrine would look like, especially with the chance of people coming up with their own interpretations.