A term describing the quality of being "off-the-record" would be ideal: like "off-the-recordness", but one that doesn't sound silly. And unfortunately there either don't seem to be any "rights" to be off-the-record in any context, they are overruled by "legitimate interests" with trivial ease, or come with "consequences" (the last two in case of the GDPR, for example).
If there's anything useful that came from the discussion with @whatiswrongwithyou@lemmy.ml (to answer your other reactions too), is that "anonymity" might actually be a reasonable fit, that is if:
data couldn’t, in any way, shape or form and without measurable confidence, be attributed to a person (or context related to them: a car, or a specific shirt worn that day, being examples); then details about one’s private life couldn’t be inferred, based on publicly available information.
Perhaps the only situation it doesn't account for is the tracking of groups of persons, rather than the individual. And it increasingly being mentioned in the same breath as "pseudonymization" (which does allow for re-identification: by design, or as a result of poor "anonymization" practices). I personally have no confidence in any "anonymization" post-collection; and a camera for example, physically unable to capture my likeness, being the only meaningful reassurance anonymity is being preserved.