Star Lord, aka Peter Quill didn't have the benefit of any "celestial power." He had the benefit of advanced genetic tampering by a being of significant technological capacity.
In essence, he was able to hold the Power Stone because he was the product of genetic engineering, not because he was channeling any "celestial power." He wasn't aware of his genetic capacities when he grabbed the stone the first time, and any manipulation of its power was purely instinctive.
It is likely the capacity to manipulate that power is still inherent within his genome, because the ability didn't depend on him knowing anything about his heritage or Ego or anything else.
His ability to manipulate energies on Ego's world was strictly because he was shown he could by Ego. Those are likely the only energies he will freely be able to manipulate because Ego created him for that specific purpose.
He will likely remain exactly as compatible with the Infinity Stone technology as he was before. He may remember how he manipulated the energy of Ego's world giving him the chance to not die should he touch the Power Stone again. How other stones will respond to him (should he get the chance to touch them) is anyone's guess.