As others have said, the crucial determinant of acceptability is almost certainly* consent and if it is there then no problem, if not: problem.
I’m not sure what grounds you would have to make a complaint however, since you are not the person potentially negatively impacted by the inappropriate disclosure (unless you are claiming mental distress maybe, if the details are particularly unpleasant, gruesome or upsetting). If you’re concerned and you have direct contact, maybe make sure the individual is aware of it, and from there it’s up to them to complain if they think it’s appropriate.
FWIW I’ve received such emails about a former colleague and it was with their explicit consent – in fact they had provided the detail of the update themselves and asked that we “let everyone know” so it’s not a preposterous scenario by any means.
*There could conceivably be other lawful bases, e.g. if the message includes “and Bob has now been confirmed as having Coronavirus so anyone who’s been in a room with him in the last fortnight needs to…” but it sounds like, from the details provided, consent is the only likely one here.