Pixijs' Spine support is based on our core runtimes, so it does support IK constraints. They are evaluated at runtime. The way it would work is you setup an IK constraint, which causes one or two bones to rotate so the tip of the bone (the second bone if a two bone IK) is at a target bone (or as close as possible, if out of range). At runtime, you can get the target bone and put it at the mouse position (or anywhere else) and the IK will adjust the rotation of the constrained bones.
You can see a demo of how that works here:
Spine: Demos: Inverse kinematics
Drag the red balls around and you'll see spineboy is posed in a reasonable way
that is all done by using multiple IK constraints. You can read more about how spineboy is rigged here:
Spineboy example
Sorry if it was surprising that Essential doesn't support IK constraints. You do need Professional to create and export IK constraints. However, IK constraints are in the runtimes. If it is enough that the IK is only applied at runtime, you could create a new IK constraint at runtime. You can look at how SkeletonJson creates one. If you give it a try and get stuck, post your code here and we can help.
BTW, you could open your project using the Spine trial so you can see how applying IK works in the editor. IK docs are here:
Inverse Kinematics - Spine User Guide
This video shows how the Preview view can be used to mimic moving a bone around at runtime:
Spine 3.6 - New Features - YouTube
Another way to do it is to rotate the bones yourself so they point at the mouse. This is sufficient if you just need a bone to point at the mouse. If you need 2 bones (like an arm) to bend then you need IK and, while you could write your own IK, it's easier to add an IK constraint. Anyway, the Super Spineboy demo game has some code that points bones at the mouse (and a bit more). It's quite a bit of code, but it's relatively simple. Basically you use atan2 to get the world angle you want, then you adjust that using the parent bones (subtract the parent bone's Bone getWorldRotationX from the world angle
that method didn't exist when Super Spineboy was written).
