Sauron has no feelings for Galadriel. He is using textbook manipulation tactics. He is lying. Using his words to sway the powerful elf to his side so that he has an advantage in domination over Middle Earth.
“I would have made you a queen.” and “I would not rest until all of middle earth worshipped the light of its queen” - Using promises of power to tempt her. He is trying to corrupt her as Melkor corrupted him. You can see it in his eyes that he is manipulating her; they are cold and unfeeling, not indicative of a romantic conversation.
Galadriel has no feelings for him. She was successfully manipulated, drew in with lies of friendship and false promises of power, and then betrayed once Sauron had what he had wanted from the start. She was drawn to the promise of power that was never intended to be given to her.
I beg of you all to use your fucking eyes and learn to read body language. If you insist on simply taking all words as true, then one day you may also be victim to manipulation and not realize it. It is extremely dangerous to take all words at face value.
Look at Sauron’s eyes as he speaks those lies. They are cold and unfeeling. A tell of his deception.