What do you think the biggest change in mindset is to take advantage of Java9's Modularity features?
I'm speaking from the perspective of a Web Developer. Should I revisit the way I design Web Apps?
Servlet containers don't support modules yet, so if you want to leverage modules, a good start would be to run your app from a main method, bootstrapping a web server from code.
There are many ways to accomplish this, but Vert.x is one of my favorites and already supports running on Java 9.
From there, decouple your code into multiple modules. Services, as described in chapter 4 of the Java 9 Modularity book is a really nice tool for this.
How to slice the code into modules really depends on the situation. One question to ask yourself is "how do I expect changes to the code"? If for a single change you need to touch multiple modules, this can be a sign that module boundaries are incorrect.
You can often slice based both on functionality (e.g. different "things" in a rest API), and also technical concerns. E.g. web vs data storage.
As a very trivial example:
This is obviously just a starting point. Ask questions like "do you expect to make changes to "books" without requiring changes to authors?" and "do you want to have the flexibility to have different storage providers?".
There's always a balance to be found. Ending up with modules that literally contain a single class usually isn't great, but a module that changes every time you add something to the app is a smell as well.