So, I’ve seen many posts saying using new official battery case for X/S (Max) decreased people’s battery health, like 3-5%.
If anything, a battery case will slow the battery degradation of the internal iPhone battery because it significantly reduces the number of charge cycles the internal battery goes through (in an approximate way, instead of charging your phone battery twice a day, with a battery case, it might only get charged once per day because for the first half of the day it is essentially plugged into a power source, the battery case). Sure, any phone case, in particular a thick one, will make heat dissipation harder and thus might slightly affect the battery health.
But keeping your phone plugged in at 100% battery capacity for roughly the first half of the day (which is what a battery case does) will have practically no measurable effect. You'll very likely still exercise the battery every day (if you were to get by with only the case's battery for anything close to a full week, you'd have no real reason to actually use the battery case daily). If keeping the phone plugged in at 100% battery for part of the day would be detrimental, people would start recommending to not charge your phone overnight (but either in the morning or evening, depending on your schedule). What might happen is that you much less frequently (almost) completely deplete the iPhone's internal battery. But if you are worried about that, just intentionally deplete it once or twice a month.
In regard to the reported 2 to 3% drop in battery capacity, that in all likelihood is completely incidental (ie, due to other reasons that just happened to occur at the same time people started using the battery case, from normal degradation that just happened to pass some thresholds that made it visible on the percentage scale to new OS versions that slightly changed how things are calculated). It is naturally also possible that the different discharge-charge pattern simply triggered an artefact in the calculation of the battery capacity that is largely artificial without reflecting any real decrease in capacity.
