I think this question ought to back up and ask itself about what it means by “mattering”. What would it mean to matter or not to matter? Does it “matter” if something matters or not. And if it’s questioning whether mattering to oneself matters or not… when would something “matter otherwise”, and is there a higher level of mattering than mattering to individuals? And what is “existence mattering”? Most of this seems like a trap of thinking, and seems to me more about confusion about what matters to the person asking these questions.
In particular, the idea that there is a universal impersonal quality of mattering or not, sounds to me like a toxic shaming thought pattern, and a set-up. Maybe a sign of depression?
It’s a set-up in that it presupposes there is something called “matters otherwise” that is real and more valid or important than “I care about it” (and that invalidates your own caring if it disagrees), and yet “matters otherwise” is defined by what, if not nasty shaming messages from sour cynical others who would be happy to off-load their worries by validating your self-doubt? But “matters otherwise” isn’t even a defined thing – it’s more like an imaginary cloud of fear of judgement and shame.
I suggesting you ask a contrasting and more affirmative question (of yourself) such as “what do you authentically care about?”
If you’re depressed enough that the answer to that seems to be “not much” or “I don’t know”, then you may want to talk about this with a psychiatrist. (Even though our culture likes to shame even THAT, but it should not. q.v. Depression.)