Okay to bury old carpenter ant infested firewood?

Here's a photo.  I left a few inch margin so it wouldn't touch my brand new raised bed.

Planning on doing one more layer of wood, several branches from tree we cut down recently.

I would put them standing up. I think it would wick water up from the ground higher into the bed.

I wouldn't worry about carpenter ants much. They might leave now that their tree is cut down. If they don't leave you could try adding some clear plastic or glass to the top for a few sunny days. It might raise the temperature enough to persuade the ants to move. Otherwise, I would just add the other sticks, soils & mulches & then plant on top of their little ant heads. Some diatomaceous earth could be spread around but that will kill them. Ants are actually quite helpful in building soils.

Fire ants are a different story. They are very aggressive but I've never known a carpenter ant (in my limited experience with them) to bite people.

I suggest leaving them on the ground for a good soil to wood contact on the base. Think of it as a wooden sponge & a future worm hatchery. Vertical would work too but beware that if they stick up too high the moisture from the inner hugel will evaporate quickly. Please make sure there is at least a couple inches of soil above the wood. With a couple inches of mulch above that.