It is the truth that you are not required to disclose any information about medical situations of your own or your family, or any related to familial status, including even the fact that those issues exist or are medical in nature.
How else is one able to exercise their rights in circumstances like this without some mild obfuscation? "Providing care" is saying enough to signal that it is an issue which is likely medical in nature, without disclosing anything about your own medical condition or circumstances, which is your right. If your issue is only "for a loved one" then maybe you have a point, but you should have no issue with "I was a full-time care provider" and now we're just mincing words.
The goal is to explain enough to make it clear the question is related to medical conditions or familial status, so that the legally well-trained interviewer knows not to pry any further, and the interviewee who knows their rights has a perfectly good way to avoid discussing it any further if the interviewer asks for more information.
"I'd rather not discuss details about that, as the details are personal in nature and not in any way relevant here." That's all you should need to say.
I have seen situations evolve from privately disclosing some information about medical issues as a professional courtesy, into supervisor asking for updates as a logistical concern, and later unwanted discussion that continues as a matter of personal empathy, and then sometimes even more inappropriate discussions between parties that are not involved, or more public than you wanted; conversations that you wish wouldn't have ever started, over things that should have never even been an issue that needed to be discussed in the workplace.
My advice is to exercise your rights and avoid this as much as possible, which is to say, hopefully avoid it altogether.