Firstly, to be strictly accurate, the data here will not be anonymous, only pseudonymous.
But in any case, we are talking about a long list of often very specific observations for almost everyone included in the data set. The chances of even supposedly anonymised data with that much detail being subject to reidentification are quite high, and there are plenty of organisations that might be able to infer enough to do it, by comparing against other data sets they already hold.
There is no way to know, because it's impossible to quantify either the expected costs or the expected benefits.
On the benefit side, there is simply no way to know what good things could come from giving the right person easier access to this data. Maybe the only thing between us and a cure for ten different types of cancer is a one-week number crunching exercise by the right university research group. Maybe we'll go twenty years and no big advances will result that wouldn't have happened anyway.
On the cost side, as ever with privacy, most of the real damage in the event of a breach isn't likely to be directly financial. What is the cost to a 20-year-old struggling with their identity if information about their sexual health leaks and betrays their situation to their friends and family before they want to be open about it?
How many jobs might be lost by women in their 30s or 40s because someone at the potential employer discovered they'd been having treatments that could be related to pregnancy or fertility in recent years and took steps to avoid hiring someone who might need maternity leave soon?
What might happen to your ability to get health or travel insurance ten or twenty years from now if you ask your doctor today about a symptom that is probably nothing but could be a sign of a serious condition? Or to your children's ability to get insurance in the future, if you ask about a symptom that could relate to a hereditary condition?
How many people, fearing the answer to these kinds of questions if their health records are shared, might not ask the doctor about something potentially important at all? How often will that conversation that never happens prove to have devastating consequences because a serious condition then went undiagnosed and untreated? A chilling effect on doctor consultations alone could easily cost many thousands of lives. Just look at the big drop in the number of urgent referrals for people with potential cancer symptoms since the COVID restrictions have meant relatively few people are seeing their GP in person.
The only thing we really know is that this is probably a one-way trip. Once Pandora's box is open, it is unlikely it will ever be closed again. And we're being asked (or not, apparently) to take that trip based on vague, hypothetical future benefits, without any reference to the potential dangers, even though there have been quite a few examples of confidentiality breaches arising from sharing this kind of data in the past.
I suppose a cynic might say the actual cost/benefit right now is therefore infinite, because in the absence of better arguments and data about the benefits, it's prudent to assume a division by zero.
But in any case, we are talking about a long list of often very specific observations for almost everyone included in the data set. The chances of even supposedly anonymised data with that much detail being subject to reidentification are quite high, and there are plenty of organisations that might be able to infer enough to do it, by comparing against other data sets they already hold.