hi prev that i don't know. one of my special interests is christianity (please note here: i am an atheist (ex-catholic) who also does not believe in sin.)
whether sin is an action or a state of being is actually a pretty interesting question! at least in my youth group we were taught that sins were essentially actions that brought you further away from yhwh, mortal sins being actions that could permanently, like, sever your bond with yhwh (though im getting off track because mortal sins are their own discussion, and are not a prodestant beleif). all this to say that, while sins were defined (in paraphrased terms) as desired, utterances, or actions commited against yhwh/the holy order, sin could could be interpreted as the state of being away from or seperated from yhwh. as in one could be in a "sinful" state.
furthermore, in addition to this there is precedent for sin being something one can "do" passively. one way can be through inaction, as opposed to action. evidence for this can be found in a part of the "pennitential act", a part of catholic mass where everyone in unison asks for pennance, where they say "... I have greatly sinned, in my thoughts and in my words, in what I have done and in what I have failed to do, ..." . failing to do something, or taking inaction, can be sinful.
though, more pertinent to the topic at hand, i believe another way to sin passively is by being a certain way, states of being can be inherently sinful. this gets kinda messy because, most states of being that may be considered sinful require a sinful action to enter. it kinda has to be some way that you are born. though apocryphal, perhaps nephalim (the byproduct of inter- breeding angels and humans) could be a separate example of a sinful existence, as they are not "of yhwh", and cannot have a connection to yhwh like humans do. though, what might the church have to say about the inherently sinful nature of humans?
now i get to talk about the thing ive wanted to bring up the whole time, original sin!!! the catholic church beleives that all humans (with i believe the sole exeption of jesus's mother, mary) are born "tainted" with something called original sin. regardless of whether or not you have ever actively committed a sin in your life, you would have original sin. this is why catholics baptize their babies, to cleanse them of this sin, because otherwise they would go to hell in the case of an unexpected death. but.. what is original sin really, where does it come from? original sin comes from the actions of adam and eve (you probably know the story), eating the fruit of knowledge, and being ejected from paradise. they were then tainted and became responsible for their actions (whereas before they were wholly innocent). one could say this is when they became "human" as it is understood today. in fact i don't have quotes on me again, but humans are considered inherently sinful creatures. as well, worldlieness is something inherently sinful.
and theres something to be said about the story of adam and eve being similar to a tragedy, by their human nature (represented by the serpent) it was inevitable that original sin would have taken place (they could never have fully followed instructions, and they always would have been ejected from paradise. and yhwh knew this) of course biblical literalists (almost all christians) really hate parable/fable-like interpretations of the old testament (particularly of the book of genesis) so its hardly discussed, even though its probably how ancient jews treated it so. its whatever this is a tangent just about something i care a lot about.
um. all this to say. i think that in christianity, being human is inherently sinful.
but under a Catholic interpretation, is our greatest sin being human? if you consider original sinto be our "greatest sin", yeah. pretty much. being human is what causes sin (it should be noted that sin is something typically unique to humans in Christianity, animals cannot sin and sometimes (the bible is inconsistent on this) angels cannot sin (but lucifer sined. so.) also whether or not demons/malevolent spirits can sin is something i don't know enough to get into. so uhhhh. yeah. though theres interpretations where there are greater sins that one can commit. mortal sins. but you could say we can only commit mortal sin because we are human. but this just kinda goes around and around.
end note disclaimer/reminder: i am not christian or catholic and do not currently agree with any of the beleifs therof which i shared. i don't think sin is real and i think the concept is inherently harmful and makes for a shit system of morality. this is all for the sake of discussion of the christian/catholic faith, and is just the ramblings of someone with a special interest. also if anyone knows something that contridicts something i said, please tell me! im always open to learning more.
