British Royal Jewels of the Past 2: 2022 -

[An Ard Ri]

I think William would have worn his coronet for the Coronation if it had been a coronation where Coronets and Robes had been worn.

I think the only time we could see William in his robes and with his Princely coronet is if William would pose for a formal painting of him as Prince of Wales and the Coronet was placed beside him on a table!