How should I go about connecting a switch's ground wire to this apparent grouping of ground wires?
The old dimmer is not properly connected to ground (an attempt was made, but it's not good workmanship...)
The grounding wires are crimped (which seems to be a popular method at some places and times for grounding wires, I assume because someone felt it saved 3 seconds per box or something) but the old dimmer grounding wire is not in the crimp, it's just jammed between the crimped wires.
If one or more of the grounding wires that are in the crimp stick out far enough on the other side of it you can use a wire-nut to properly connect your new dimmer's grounding wire. Can't see if that's the case since they appear to be behind the other switch in your pictures.
If not, you can cut off the crimp and use a wire nut to connect all the grounding wires and your new dimmer grounding wire.