…is because he wasn’t loyal to it in the first place. His path and the Empire’s path have joined for a while and will separate when time comes.
If you remember Legends, Thrawn has never been a true Imperial either. He actually built an Empire of his own, integrating Humans and Chiss and so many other races.
So, my prediction for S4: Thrawn understands that the Death Star project will be the end of the Empire considering the growing turmoil, stages his own death with the help of Rukh (a logical go-with and awesome irony, I’d love to see that) and leaves for the Unknown Regions to prepare the soil for the First Order so that the great military force of the Empire will not be entirely lost.
Perhaps he somehow takes the Eclipse with him as well.
There also other threats the the First Order must contend with. Who knows what they are?