Sharing ground wire between two dedicated circuits

Functionally I think it is fine.  I don't know if it meets the code. Others will likely chime in.  If you are having an electrician install and a building inspector inspect you need to make sure both of them are ok with it.

As long as both circuits originate from the same panel you can share the ground -- if your jurisdiction uses NEC 2014 or later.

Note that 10/3 Romex has three uninsulated wires (black, white, red) and a bare ground, 4 wires total. The insulated red wire you are making a ground must be wrapped with green electrical tape where visible (in the outlet box, panel or any intermediary junction box).

If you are using metal boxes, you can use the bare ground clipped/screwed to the 10/3 box and the insulated (taped green) conductor on the 10/3 receptacle ground screw. You can then tie the 10/2 ground from the 10/2 receptacle (or metal box ) to the 10/3 box.

If plastic boxes, then run the #10 insulated "ground" from receptacle screw to screw and clip the bare grounds back to the orange insulation.

gs5556, amazing answer thank you

Is Romex 10/3 good for the dedicated Circuit?  I was told the ground was insulated, which seems like a good idea. True?

I was also told 10/3 better to use vs 10/2, because the ground is insulated and 10/2 is not. So it's all a bit confusing

@emergingsoul If you’re going to spend this kind of money for two dedicated circuits, why not just spend a tiny bit more for the best? If they are truly dedicated circuits, with dedicated circuit breakers, their grounds should both never intercept with each other, until they reach the circuit breaker box (aka load center). Instead of using Romex, go a step further, and use Aluminum Armor Clad for Healthcare Facilities (AC-HCF). It’s the absolute best choice for Isolated Ground A/V systems. The biggest benefit is that the average proximity of the hot conductor and the neutral conductor, with respect to the isolated equipment grounding conductor, is nearly equal, virtually eliminating ground voltage induction (GVI), even on long runs. If you go that (AC-HCF) route, I’d also use isolated ground outlets.