Hello!
If I am not mistaken, you may be confused with the use of “had better” as in “you’d better go to bed before you mother comes home”. There is no such use of “would better”, at least not to my shallow knowledge. I consider the “had better” question as an idiomatic one rather than a grammatical one. When constructing a sentence with “You / he /they had better +verb ...... “had better” has no ties at all with participles. I think if there is any error in my example, it may be the notation “future” at the end of the sentence. Otherwise, I believe it is correct.
I have understood that now. Thank you Goodman, Paco.
Jake