How do I cope with the unpaid, invisible work of peer review?

You can review anything in your field with real authority. And you are tired, because that authority gets spent on unpaid, unseen labor that quietly holds the whole field together while no one thanks you for it. That weariness is legitimate. You are carrying a load the system depends on and refuses to name. The work matters even though it is invisible, and that is exactly the trap: because it matters, people who care keep doing it until they burn out. You are not obligated to personally hold up the entire structure. Being able to do something well does not mean you must do all of it, endlessly, for free. Set a sustainable limit. Decide how many reviews you will do in a year and hold to it, so your generosity does not become self-erasure. Say yes to the ones that genuinely matter to you and no to the rest without guilt. The field needs you for the long haul, and you last longer by giving deliberately than by giving until there is nothing left.