"They'll think I want something"
This one is about the reading. You say to your manager that the way they handled the restructuring was fair, and you watch them wonder what you're after. You tell your neighbour that their front garden is the best on the street, and now you're the person who's softening them up before asking about the fence. A compliment, in this belief, is an opening bid, and everyone knows it.
Some compliments are opening bids, and people can tell. What they can tell it from is what comes next. If "the restructuring was fair" is followed by "and about my hours", it was a bid. If it's followed by nothing, it was a report. The reading you're afraid of depends on the ask, and you don't have one. The thought about the garden came with no fence attached.
There's evidence on which way people actually read an unexpected kind word, and it's from a close cousin of the compliment. James Dungan, David Munguia Gomez and Nicholas Epley ran four studies, published in 2022, on messages of support, the "thinking of you, hope the week's been all right" sort of message. People who sent them to someone they knew, or expressed support to a new acquaintance in person, underestimated how positively the other person would respond, in the same direction as the compliment studies. The reason they found was a gap in what each side was attending to. The sender was thinking about how competent the message looked. The recipient was reading it for warmth. Nobody on the receiving end was scanning it for the angle.
I'd take from that something specific. When you're deciding whether to say the good thing, you're imagining a suspicious reader, and the suspicious reader is you, checking your own motives. The actual reader isn't doing that. They're doing something simpler, which is noticing that somebody thought well of them and said so.
Two practical notes, and these are mine. First, don't attach anything. If you have a request for the same person, keep it for another day, because the compliment and the request in the same breath will be read together, and rightly. Second, don't over-explain. "I'm not saying this because I want anything" puts the idea in the room. Say the thing and stop. A compliment with nothing after it is its own proof of what it was.