How does Shadow Sneak Attack Progress? Is it just 1d6 forever, or does it progress on 11th and 15th levels?
Does Shadow Sneak Attack stack with Strategic Strike? It specifically mentions how it interacts with Sneak Attack (use only the higher precision damage), but Strategic Strike isn't Sneak Attack.
First, Shadow Sneak Attack doesn't progress. It's 1d6 forever.
You gain the sneak attack class feature, except you deal 1d6 precision damage regardless of your level. Sneak attack from multiple sources isn't cumulative. If you have sneak attack from more than one source, use only the highest number of dice when you sneak attack rather than adding the amounts together.
However, fortuitously for you, it does stack with your Strategic Strike. Precision damage stacks with itself by default, and where there are exceptions, they're called out specifically (as above).