Angels are people. What they are not is human.
Purgatory is Catholic dogma.
Limbo is a theory that was put forward by Catholic theologians centuries ago, but it has never been elevated to dogma.
Kinda depends on how you define ‘people’, doesn’t it?
And IIRC, there’s been debate about the degree of free will that angels would have, so maybe they’re not “people” as we’d conceive of them.
‘Person’ in theology has a specific definition. It is usually rendered something like ‘individual substance of a rational nature.’ where individual means distinct and unique, rational means possessing of intellect and substance means hypostasis or underlying ‘realness.’ (Of course, this definition is why traditionally religious people didn’t have as much of a problem with abortion and it was only with the advent of scientific knowledge of development that they did, but that’s a different discussion.)
If we assume a traditional understanding of angels (which certainly one can argue against), then they are individual, they have ‘reality’ and they have intellect, so they are ‘persons.’