Is there a way to bake deformer graph animations in level sequencer into an animation sequence

Yeah the first thing I noticed is that the length to deform variable pin on the add deformer node is set to 0, which basically turns off the squash deformer since there is nothing to deform, something like 100 might make sense and from there you can then tweak the factor pin.

Another thing you can try is double click the node title of squashstretch deformer node and it should open up a deformer graph asset called dg_function_squashstretch, and if you use your sphere mesh as the preview mesh in the preview scene settings, does it show deformation in the viewport? Also if you go to the update graph in the same asset, there should be an example graph setup.

And thanks @jakesjordan for the detailed steps! Pretty much exactly how it is expected be setup. The add deformer node simply first collects variable values during rig forward solve and separately at render time(unrelated to rig solve) use those variable values to drive deformation.