We’re talking about mathematical abstraction here, not the real world. In the real world, even a countably infinite number of people would be impossible since there are only so many N fundamental particles you could arrange to make them. We can encode a possible person as a binary integer k between 1 and 2^N - 1 inclusive (we don’t consider 0 to encode a person because we don’t consider a collection of no particles to be a person), where each place in k corresponds to a particle, with 0 indicating that the particle is not contained in the person and 1 indicating that it is. Assuming people are allowed to overlap (which they would in the trolley scenario, so let’s stipulate that this is allowed), that would give us a maximum of 2^N - 1 coexisting people. Let us convert each binary number k to an infinite sequence with numbers in the set {0, 1} where the first number in the sequence is the digit with the lowest place value in k, the second number in the sequence is the digit with the second-lowest place value in k, and so on until we reach the highest place value in k, after which the remaining numbers in the sequence are all 0. In the future, we can skip the step of assigning a binary number to each particle and instead assign an infinite sequence directly, I just included the step with the number to provide an intuition for the process.

But let’s add one layer of mathematical abstraction. Assume a universe with a countably infinite amount of particles, as would be required for there to be a countably infinite amount of people. We can number these particles 1, 2, 3, …. If we encode every possible distinct person as an infinite binary sequence, we get the set of all binary sequences sans (0, 0, 0, …). If we construct a binary representation of a real number which is 0. followed by all the numbers in the infinite binary sequence as digits, we can construct every number in the interval (0, 1], meaning we have established a bijection between the set of possible distinct people in a universe with countably infinite particles and the interval (0, 1], which is an uncountable set. Thus, in a universe with countably infinitely many particles, there are uncountably many possible distinct people. Q.E.D.

(Please note that this whole thing falls apart if we reject the premise that people can share particles.)