Can I run a new circuit in the same conduit as ground cable?

I'm fairly sure that conduit fill rules (and your own swearing) will prevent adding a UF cable to a 1/2" conduit that has anything else in it. I ran the calcs for 1/2 EMT (which has a bigger hole) and indoor NM (which is generally smaller than UF) on my own job and determined that where the only thing in the conduit at all was a chunk of 14/2 I could use that if I wanted to (I have lots I won't be using otherwise.) Lacking a good measurement on UF I'll let somone else write a better answer with the calcs for that, but it won't fly as far as I can tell.

I make 1 #4 THWN (I see green insulation) as taking up 37.7% of your 1/2" Sch 80 PVC conduit all by itself.

A cable is several wires that are factory assembled. A "circular inch" is the area of a circle 1" diameter. A "circular mil" is the area of a circle 1/1000" (1 mil) diameter. (so there are 1 million circular mils in a circular inch). This unit is used a lot in sizing larger wires, but I find it rather useful in conduit fill calcs.

The interior of 1/2" PVC Sched 80 conduit is 0.546" or 546 x 546 = 298,116 circular mils. (or 0.298 circular inch).

Hold on... is this leeegal?

Yes, a branch circuit can share a conduit with a Grounding Electrode Conductor. In that thread you see a great deal of arguing about how bonding works, but that's because they are using metal conduit. You're in PVC so you sidestep the discussion. Nobody challenges the idea of a branch circuit in a conduit with a GEC.

The grounding electrode and branch circuit need to go their separate ways. You can't do that in a conduit body (at least not this particular type). So this conduit body must be changed out to a junction box or more flexible conduit body. Remember the branch circuit needs a conduit "stub-up" down to 24" burial depth. That is probably incompatible with the bare GEC wire routing.

You are not allowed to cut and splice GEC runs, so you will need to pull it out of the conduit for this modification and then put it back in. You are also not allowed to assemble conduit around cable, by the way.

UF cable doesn't work...

With oval shaped cables, the wide dimension is used for conduit fill. Because it twists.

With 2 things in the pipe (cable and ground wire), we are allowed to use 30% of that or 89,435 circular mils.

The #4 bare ground wire is .232" diameter at its widest. That is 53,824 circular mils.

Leaving 35,611 circular mils to work with. Square root of that -- the largest cable that will fit is 0.188" across in the wide dimension. No cable exists anywhere near that small. Not gonna happen.

But let's crunch the numbers anyway.

• A 12/3 UF cable is .626" diameter at its widest, so 391,876 cmil. So 445,700 cmil, divide by .3 and we need a conduit with 1.485 circular inches, or 1.218" ID on the conduit. So you'd need 1-1/4" conduit. Wow!

• A 14/2 UF cable is .423" diameter at its widest, so similar math: 1" conduit.

...try it with THWN wire

Okay, cable in conduit is always a stupid idea, and the above is a picture postcard as to the reason why. Let's try it with THWN individual wires, at least through the pipe. Since we have 3 or more things, it'd be 40% or 119,246 cmil. The #4 bare ground wire is still 53,824 cmil, leaving us 65,422 cmil to play with.

A #12 THWN copper wire is 0.127" or 16,129 cmil.

16,129 x 4 wires (hot hot neutral ground) = 64,516 cmil. And we skate under by a nose! If it were closer we could use a solid ground wire and strip it bare.

OK, so we've got our 12/3 multi-wire branch circuit through. Now we have to bury it.

Routing to the shed

Since you said "direct burial", you must trench down to 24" of cover (so 25" depth). Really. As discussed above, you will need a junction box or more versatile conduit body there. Loose THWN wires can't be buried, so after you're through the hole, you will need to splice the THWN wires to a 12/3 UF cable that can be direct buried... and that means, it will need to be a junction box, not a conduit body.

You cannot use the 12" exception for GFCI protected circuits, because that only works on plain 120V circuits, and your planned/future multi-wire branch circuit does not qualify.

If you run conduit to the shed, the news gets brighter. You need conduit for the stub-ups at both ends anyway, so if you simply stay in conduit in the trench, then you can just continue the THWN wires in the conduit. No splicing and you only need 18" burial depth.

Rigid conduit only requires 6" burial depth (12" under vehicle pathways), the stuff is hella expensive at over $2/foot Of course, you're only going 10 feet. It will take a friendly hardware store who threads pipe and a couple of runs to see them once you have lengths worked out.