The signaling value comes from the cost of the diamond. "Wasting" a lot of money on something so impractical proves you have wealth to waste, and spending a lot of money on a gift to a loved one proves that person is valuable to you.

Pay less for a synthetic and admit it, and you've signaled a lack of sufficient wealth to buy a real diamond.

Pretend a synthetic diamond is real and you're deceiving people.

Either way the synthetic diamond is signalling something undesirable (to the target market for diamonds) precisely because it costs less.