Your question is an interesting one, and I am not surprised it is still floating around.
CGel can reasonably treat the who used in this type of context as a relative pronoun. It would involve something like understanding an unstated "..is who I am". That is a reasonable way of looking at it. Similarly, you can argue that it operates as an interrogative pronoun. In that case "who I am" is indirect (reported) speech, where we are to understand "..is who I am." Either is defensible.
The first and obvious thing to say is that despite the now almost universal use of this fashionable idiom, dictionaries like Merriam Webster and the Cambridge English dictionaries do not seem to deal with it. I can tell you what it means (as if you didn't know already). Whenever its first use may be, I doubt (from memory) whether it can be found before 1990, and possibly not before 2000.
Understanding the expression has very little to do with grammar. I mean that whoever its first users may have been, they are unlikely to have had a precise grammatical analysis in mind. And whoever they were who caught onto and spread it around the English speaking world were not interested in the grammar of it either. The fact that this saying is grammatically troubling is probably one reason for its catching on and spreading so widely. What it is, I have learned from internet searches, is a meme, and indeed a locus classicus of a meme. (By the way, locus classicus was probably a sort of meme of its own time (which ended during the second half of the 20th century). It was known then (in my younger years) as a Latin tag, widely used by academics barristers and senior civil servants till the 1980s, when the British civil service and other banned them from their publications and communications!)
The expression "it is who I am" is used more than once by Chris Tomlinson, who has a song which uses the meme over and over again:- https://babylonbee.com/news/im-chris-tomlin-its-who-i-am-16x---op-ed-by-chris-tomlin. Every verse consists of one repeated line as does the chorus (refrain)
I'm Chris Tomlinson, it's who I am.
I shall not discuss the literary merits of this particular use of the meme. But one thing is obvious, and that is that there is nothing grammatically troubling about it. The use of the word 'who' may be interrogative or relative. It tells you the identity of the speaker. Once I know your name is Chris Tomlinson, I know part of how to find you again. Though there are many other people of that name, it's a good start. It gives me information about your identity.
Then there is a song by Chris Young called Who I Am with You. The song begins with an account of his making a bad start in life: a rolling stone, and in general not much good.... until he meets his beloved, when, in a rising climax of volume and pitch, he declares that
A better man is who I am with you.
This is different. This is linking his quality as a person to to his identity. But of course, if you ask the lucky girl who her boyfriend is, she is not going to answer: "He's a better man", or "a good man". She certainly is not going to have much luck asking any of her friends whether they know where this better man she met up with on holiday might live. "Do you mean to tell us you didn't find out who he was?" they might ask incredulously. So there is something queer about this locution.
The expression is often used to lay claim to particular personal qualities as their identity, or part of it. Someone can also use it to assert that some pursuit or avocation is so important to them as to be part of their identity: "musician/plumber/safe cracker/parent ... is who I am". Without it I am nothing. Before the meme came along, people would say "Musician is what I am, or "A better person is what I am".
The meme is, in other words part of the contemporary identity culture. This meme asserts a person's right to the things that are most important to them: things neither the state not society have the right to take away. This may involve personal qualities, possession, avocations or group memberships, national, ethnic, religious, gender and so on). Such assertions are, to be sure, likely to be challenged by most people at certain points: people are unlikely to find many accepting an assertion that a safe cracker, multi billionaire, serial killer or prime minister of the UK is "who they are". It raises questions, much debated, about whether a people can claim any kind of right to anything they lay claim to as "who I am". But this is not a matter of English Language Usage.
Aside from that, the expression (meme) succeeds by being arresting. And part of that arresting quality has to do with a (let me call it) grammatically stretched use of the relative or interrogative who to cover "what kind of".