I appreciate that you're trying to define it and want us to comment about it. I'm going to comment and try to define it by myself.
sex identity could be multiple things, just like the meanings you listed. however, since it's scope is so ample, when we use sex identity solely and the context talks about the body, it's often to show that the physical body exists regardless of the words we use to denominate or classify it. does that make sense?
sex identity is used less formally than gender identity, and it's more common to see the noun phrase "sexual orientation identity" than the univocal concept "sex identity", at least when used among mainstream activism. because in media and nowaday lectures aimed at people who don't understand much about the community, or from countries where the word gender is unusual, "sex identity" can appear as synonymous to "gender identity". tbh it's confusing to use this term deliberately, and I've seen people using the word "status" instead of identity. however, in the official languages of my country, "status" is more associated with the law, documental things, or computational stuff. that's why I don't use it a lot.
"intersex status", for once, is a term to refer to intersex as an identity, while "intersex variations" to refer to bodily traits (internal/external, and internal here means inside the physical body, and external refers to the apparent traits) or given condition or a set of conditions. status can be recognized by oneself and by others.
about your definition: sex identity in our blog is used totally separated from gender. you can gender your sex traits, and gendering one's sex can be a form of sex identity (eg. I possess a male nipple and a female nipple; I have male genitalia despite producing female gametes). when you gender your sex traits, it's about bodily autonomy and identity self-determination. it's an option to use specific language (eg. my nipples are differently sized; I have a cavernous large phallus despite being oogenic/macrogametic). it should be noted that when using specific language, not everyone will know what those words mean, typically usual to medical studies, and some of them are opt-in like referential language, because it's arbitrary or biased to talk about a indeterminate quantity in a given population. not everyone with a phallus will perceive it as penile or clitoral, or call their pectoral parts as chest or breast, for example.
is sex modality an identity? it can be a descriptor and an impermanent identity that one avoids using situationally, for example. but it definitely can be an identity, or just a relation between how one previously was and how one currently is, between the desired sex traits and current sex traits. it can be about sex sonance too, if one interprets it's tied to.
varsex is sex variance, meaning that it's a dispersion from the expected sex traits. in simple terms, in encompass intersex and altersex statuses. does this stand beyond status? certainly! a group of two people is sex-diverse, regardless of their sex identity. how does that make sense? because even twins are different, so is our genitalia, they all appear dissimilar. except when we talk about groups of people classified by identity or defined with more ample criterion or wider scope. for instance, these two individuals can both carry vulvar tissue. but that depends on how we interpret the word diversity. oh, and there are protsex/protosex people as well, they may or may not be varsex I guess.
sex identity is sex? it depends, it can represent sex. but they are different things. if sex is defined by gametes we produce, are sterile/infertile people exempt from it? it really varies of the context you're using the word sex.
spectrum may not be the best analogy. and:
gender & sex can be the same thing for some people. for once, intersex is the gender of many people, and man is the sex of many people too. despite that, they can be distinguished and therefore different things. we can say they can be interconnected or influence each other, but the names/labels/terms are often used documentally and it's inescapable to use them interchangeably sometimes. it's understandable to use only one word for both things, especially when there's only one word in a given language for either sex or gender of theirs.
questions: is "result of injuries" applicable to endogenous traits (since you mentioned illnesses) or specifically about artificial/surgical intervention (therefore mutilation)? would physical changes apply? would it include willingly wanted/planned modifications?
