A lack of theistic belief says nothing about what you do believe in - if you believe in anything at all (if such a thing is possible).
It is a term solely about what you don’t believe in, which in this case just happens to be God/gods.
What you do believe in as an atheist can range from literally anything to any combination of things, just not God/gods. Not believing in that one category of things (God/gods) is literally the only thing atheists have in common.
This is the standard “new-atheist” argument.
It pretty much wraps up the exact way in which “theism and atheism (are) not the same” exhaustively and sufficiently.
Theism is of course unfalsifiable, and probably intentionally so, and no doubt this isn’t even a problem for thinking/honest theists. Christian clergymen with any intellectual ability, who seem to have wrestled with all the issues with their religion over their lifetime don’t even bother to argue that their belief is “knowledge” - they admit it’s meant to be blind faith and that’s the whole point.
Likewise there isn’t going to be any evidence that could prove atheism, because that could only ever be evidence of absense, but there can be logical proof of atheism if some essential characteristic to God/gods is definable and logically contradictory with something that is necessary.
My proof that God doesn’t exist defines this essential characteristic as being at least in part beyond human conception.
This is logically contradictory with the human ability to believe in anything that fully qualifies as God, because entirely within human conception nothing can ever fully qualify as God i.e. something that is at least in part beyond human conception.
The conclusion necessarily follows that anything humans believe in is something less than God, that doesn’t qualify as such, and therefore isn’t God - making God-belief by humans impossible. God doesn’t and cannot exist to us.
But no matter how convinced I am of this syllogism, or how obsessed any atheist is with their lack of belief in God, of course they can still be a fully-fledged atheist. Any common ground between obsession and religion doesn’t make an obsessed atheist religious “and therefore not a fully-fledged atheist”. And the assertion of a premise that is proven false isn’t a belief in the existence of the subject of that premise.
At best, atheist argument posits a provisional existence of a definition of God, which they believe to be true, in order to disprove it.
If that makes atheists theists or “bad” atheists, then argument against anything is proof that it exists - therefore everything logically exists. Including logically impossible square circles.
At best, positing a premise awards “some degree” of existence, but in light of the above, it’s illogical for that to constitute belief in that something based only on that degree of “existence”.