And something about the water coming into the toilet bowl and equalling itself out and drips back into the drain and hits the copper making this noise.
In simple terms,
Never heard such a thing, nor does it make any logical sense.
When a toilet is flushed, the water in the tank flows (rapidly) from the tank to the bowl. This rapid addition of water to the bowl caused the bowl to flush and empty due to a siphon action. The flush valve closes due to the emptying of the tank. The lowering of the float causes the tank to refill. The flushing action in the bowl and the refilling of the tank are two separate actions.
Granted a small amount of water falling down a vertical pipe and hitting a horizontal section pipe could make a dripping sound. The only way that could occur in a toilet, is if the water level in the tank is to high and a small amount (very small) of water is flowing into the overflow pipe to bowl. This could cause a small amount of water to pass over the bend in the bowl trap and then down the sewer pipe.
All this amounts to, the water level in the tank should be about 1" below the top of the overflow pipe when the fill valve shuts off.