"I'd rather you didn't open the window."
I'm confused about the grammaticality of this sentence. I've learned that "rather" can only ever be an adverb, not a verb. Because I thought "rather" functioned as the main verb in sentences like the above (I'd rather + a different subject + past simple clause) , I believed this sentence and others like it were wrong and that I should use "prefer" as the verb instead. I could therefore write "I would prefer it if you didn't open the window," or "I would prefer you not to open the window."
However, I have done some more research, which included reading this post, and have learned that "rather" is still fuctioning as an adverb in my original sentence. This has confused me. What is the main verb of the sentence if it's not "rather"? It can't be the "would" in the contraction, because "would" is an auxiliary verb, which can't be a main verb. The impression I got from reading some of the answers on the other question was that the main verb is omitted. In that case, what is the omitted verb? I have tried to find the answer on my own but haven't come across anything definitive.