Man, you’re giving me flashbacks to real analysis. Shit is weird. Like the set of all integers is the same size as the set of all positive integers. The set of all fractions, including whole numbers, aka integers, is the same size as the set of all integers. The set of all real numbers (all numbers including factions and irrational numbers like pi) is the same size as the set of all real numbers between 0 and 1. The proofs make perfect sense, but the conclusions are maddening.
A Coulomb is basically a number of electrons, so it still very much depends on capacity. The only way it could avoid capacity dependence is if the amperage varied depending on total available uncharged capacity. That in itself is unlikely because the wires that transmit the electricity can only handle so many amps before getting too hot and melting apart, so any charging system must necessarily be constructed with intended charging capacity and rate in mind from the beginning.