WhatsApp says even the photos shared on its platform are end-to-end encrypted. When WhatsApp says encrypted I assume the data is encrypted in my device and then sent across to the recipient.

When we are sending a photo for the first time we can see the actual upload happening (if you are in a slow network), but when we forward the same picture to someone else, the upload is not happening. It happens in an instant.

AFAIK the photo would have been again encrypted with the key pair for the second recipient and then again sent to the second recipient. Since the second upload is not happening is it that the encryption happens in the WhatsApp server? Is WhatsApp decrypting the media file and encrypting it with the new recipient's key when we forward it? Can it be called end-to-end encryption in that case?

Leaving aside the WhatsApp aspect fo the question: the effect described can be achieved with hybrid encryption, where the bulk of the data is encrypted under a random secret symmetric key, and the result uploaded once; revealing that data to a recipient is performed by encrypting that symmetric key towards the recipient (e.g. using his/her public key), and thus requires very little data transfer from the sender for each additional recipient.