I am installing a ledger on the foundation here, and the ground wire from a panel runs right through it. Do I need to run this wire horizontally around the ledger, or can the ledger slide in behind the ground wire? Does it need any sort of conduit for it?

No protection needed for #6 unless subject to physical damage. You could notch the back of the ledger board a little if you want and double up on the fasteners if you think it's necessary.
Also, don't cut the wire to extend it out over / around the ledger.
Guessing you are building a deck.. pull siding and just notch the ledger board or pull out the wire so LB goes behind wire. Just make sure to flash the house to ledger
It's actually attaching to the concrete, below the siding
I'd just notch the board and leave that wire where it is
Pro deck builder here. Do two ledgers one on either side of the wire. Ledger and wire don’t interact. Only a one inch gap is needed.
Yeah I was thinking either this, or cut a groove behind the ledger board. Either way extra anchors around here is needed
Yup. But solves your problem
The ground wire is so thin I would just sandwich it against the concrete when you install The Ledger and it will indent slightly into the ledger.
Some sparky just offed themselves reading this
What's wrong with having a ground wire against wood?
I'm more worried about damaging the wire by smashing it between the building and the board
Smashing? Ground wires are sort of braided or twisted. And when you sandwich the electric you're going to be slowly tightening a bolt on the outside of the board, pulling the board Against The Wire.
You don't need any conduit for a ground wire. I would slide the ledger board behind the ground wire. I agree with the comment about flashing the house to the ledger. So many people overlook this.
I'm of the philosophy to never damage the foundation of your house.
If done right it wont cause damage