The story the other day was that the court just refused to remove a stay on the mandate pending their ruling, not that they had made an actual ruling on the mandate. Also, that case seems to be specific to Navy SEALs seeking religious exemptions, not about the Navy’s mandate as a whole.
I’m not sure if this British source even understands the legal intricacies at play here.
The Daily Mail isn’t known for in depth research... very much a tabloid. They get a lot of play because they are one of the few outlets that report on black on white/Asian crime in the USA.
On Monday, the U.S. Court of Appeals for the Fifth Circuit denied the Department of Defense’s emergency stay request, which would have allowed the mandate to go into effect as the case goes through courts.