Is Sauron Being In Love with Galadriel Actually Canon?
Non-twist of The Rings of Power Season 1's finale was Halbrand confirmed for being Sauron's current form the whole time. (The "non-" part is thanks to that being commonly predicted on Internet since Episode 1).
And it was revealed through Sauron's attempt to corrupt Galadriel in a scene which was full of seduction-like moment. Now, to get the obvious out of the way, anyone with a functional pair of eyes can see that the scriptwriters quite purposefully filled their interactions, culminating in that final scene, with romantic subtext. But at least the scriptwriters had enough taste to stop before the point, where subtext becomes just text.
In particular, if you look at what the scene states, rather than at what its details, like actors' performances, hint, it is obvious that Sauron has no romantic feelings for Galadriel and probably doesn't quite understand what romantic feelings are supposed to be.
In his first mental attack he pretends to be Galadriel's brother (whom he, by the way, killed in the past) and merely attempts to persuade her into staying aside and not interfering with the whole ring-forging business.
Only after her willpower and resilience prove to be too great, Sauron pretends to come clean, professes good intentions for the Middle-Earth (while shifting blame for his earlier crimes on his old boss), and makes her the offer which can be summarized as "we can rule together".
So it is important to note that for the series-Sauron even just attempting to sway Galadriel to his side by an – unspoken – promise of making her his Queen was more like a last-resort desperation move, than a preferable option. "He does not share power", as Gandalf said much later.
There are some grounds to say that he genuinely admires Galadriel for her power and determination, qualities that he might even find inspirational, though we can never tell for sure, when dealing with such a habitual liar. But there is no objective ground to say that Sauron in the series had even a dimmest spark of love for her – even his conversation tactics remain manipulative, trying to pin Galadriel to her words, pretend that lies by omission do not count, and isolate her.
Of course, no such sort of dispassionate analysis attempts would stop or had ever stopped fanfic writers, and, again it's not like the showrunners actually wanted to stop, rather than encourage said writers. As Sauron himself had amply demonstrated in the series, what you say and what impression you seek to create are different things.