Harry is a pawn, and that's okay.

In a vacuum, he is not worth much material (the value of material is assigned based on their average mobility, and Harry is a school-aged child with little power and less experience).

But material is not all there is to determining who has the advantage in a chess position, or else there would be no need for chess engines to calculate it. You can have advantage from your level of control over the centre of the board (the no-man's-land so to speak), from how much you've managed to infiltrate the opposite side's territory, and (very importantly) from your pawn structure. Just because a pawn is "only" worth 1 point of material in the abstract doesn't mean you can just throw it away willy-nilly; being even a single pawn down and/or getting your pawns into a weak position (or allowing your opponent get their pawns into a strong one) can be a straight-up loss against anyone who knows what they are doing. And as the game progresses and more material is traded off the board, pawns (especially connected pawns, i.e. pawns that are next to each other so that they can advance while protecting each other) become a more and more powerful resource. Not just because of the possibility of promotion at the end of the board - there are many checkmates that involve pawns

All that is probably a bit confusing but I really wish actual chess knowledge was more mainstream, because almost all the chess metaphors in pop culture fucking suck. Almost every fic I've read that used chess as an element (from the ones trying to make more of Ron's talent at chess to the ones berating Dumbledore for being a "manipulative chess master" - as if he himself weren't a piece on the board!) fucking sucks. If you know any fics involving chess by anyone who actually knows the game please recommend 😭