Beware spoilers of all the Harry Potter books ahead.
So in most of the books, all the adults good and bad underestimate Harry, time and time again. They think he is just a child and that they know much more than him. The only ones that don’t underestimate him are Dumbledore and Sirius.
Sirius wants his friend James back, and possibly remembers all the stuff they got up to when at Hogwarts themselves. He sees Harry as more a friend than someone still new to magic.
Dumbledore see the good in everyone and only really stops Harry from doing things because he wants Harry to have a proper childhood.
Everyone else just acts like he doesn’t know enough to be of use, most do it out of love and I suppose that kids generally could not help out most of the situations. BUt he kept proving himself from a young age and they still weren’t taking him seriously. Voldemort severely underestimates him time and time again, not just for his magic skills but his guile, loyalty and sheer luck.
But in the 7th book, Bellatrix gets her wand stolen by Harry. Then informs Gringotts that imposters might be arriving (although that is only speculated at). So people are finally starting to Harry seriously , or is it just because Hermione was there, people stopped underestimating her very quickly. Or was Bellatrix just covering all bases, making sure nothing went wrong. Or did Snape (or someone else) tell the death eaters that Hermione, Harry and Ron have made polyjuice potion. Since it takes a month to brew, it must have taken some time to sort out all the details. Snape suspected them, and Dumble doesn’t miss much so he probably told them.
My point is that maybe just maybe near the end people were finally taking him seriously. By everyone except Voldemort of course, people kept offering to help him but he would not listen to them, underestimating Harry cost Voldemort his life.