Pouring new concrete over existing

When new concrete touches old concrete the old will absorb the new concrete's water content, which would cause the new concrete to not cure correctly. At the same time, cracking will occur due to the fact that the two will not bond as one. Since this is a carport and is heavily loaded, cracks will occur.
The existing wood column should not touch the concrete as it will deteriorate if you bury the column into the concrete.

You are talking about the bonding agent where you would need to prep the existing slab by roughening it with 1/4" amplitude. If it was a walking slab, I might consider it since you are putting in 3" but for a carport I wouldn't try due to the loading. Also, again there will be cracking and the two will separate. Not recommended.