It's not cis passing privilege unless either
1) you're read as your actual gender but not read as trans (trans guy read as a cis guy, trans woman read as a cis woman)
2) It's your comfortable presentation/a reading of your gender that is comfortable for you (this can include being read as one's sex assigned at birth or as the other assigned sex-but it needs to be a way the person is comfortable being read)
Because just being mistaken for cis while closeted is being closeted, with all the associated pain and loneliness. Being mistaken for one's assigned sex despite being out or trying to present as one's actual gender isn't "passing" as cis, it's being plain old misgendered.
Not everyone is read as ambiguous during transition or while living as their real gender. There are a very limited number of situations/times in which someone looks at me and thinks "trans person", they are far outnumbered by situations in which people read me as a cis queer butch woman and even by sitauations where I am read as a cis somewhat girly/queer boy. I'm more likely to be called a dyke than asked why I'm trying to look like a boy (that wouldn't be a fully accurate description of my gender either). Whether I use my cane has a greater affect on how strangers gender me than how out I am to people in closer circles (I have no fucking idea of why a plain brown wooden cane screams "girl" to people...).
No, this isn't a universal experience by any means, and it's not by any means easier than being read as trans vs sorted and then read/misread as cis, but it also isn't a super uncommon way of being misgendered.
If being read as a cis person were a comfortable way of being generally read for me, then I would have cis passing privilege/most aspects of cis privilege. "X is read often as their sex assigned at birth" tells you less about what aspects of cis privilege that entails than "how comfortable does X feel about being read often as their sex assigned at birth". Being read as a cis person of your assigned birth sex is only cis privilege if you're actually cis (elements of cis privilege if you're not cis but genuinely comfortable with being read this way), if not it can be pretty brutal form of regular misgendering.