[0] https://www.navalgazing.net/Carrier-Doom-Part-1
[1] https://www.goonhammer.com/star-wars-armada-naval-academy-wa...
It's not built for hiding at all, that's what submarines are for (and that's where our nukes are).
A carrier strike group isn't meant to be stealthy. Quite the opposite. It is the ultimate tool for power projection and making a statement. If it is moving to a new region it will do so with horns blaring.
Obviously troops shouldn't be broadcasting their location regardless, but this particular leak isn't as impactful as the news is making it out to be.
At one time I guessed that too, but I've heard navy people explain that it's actually pretty effective. Imagine saying 'pretty hard to hide in North America from a satellite' - it's actually not hard because the area is so large; there aren't live images of the entire area and someone needs to examine them. Oceans are an order of magnitude larger.
A significant element of security for naval ships is hiding in the ocean. US aircraft carrier planes have a ~500 mi effective radius without refueling; even if you see a plane, all you know is that the ship might be in a ~3,142 square mile area. And remember that to target them, you need a precise target and the ships tend to be moving.
With ML image recognition at least some of that security is lost. Also, the Mediterranean is smaller than the oceans, but the precision issue applies. And we might guess that countries keep critical areas under constant surveillance - e.g., I doubt anything sails near the Taiwan Strait without many countries having a live picture.
Clouds. (Radar sats can see through clouds but can also be jammed.)
But even on a clear day, most of the people looking to target a carrier these days (Iran/hamas etc) don't have their own satellites. But a real-time GPS position accurate to few meters? That could be tactically useful to anyone with a drone.
An active fitness tracker might also give away the ship's readiness state, under the assumption that people aren't going to be doing much jogging while at battle stations.
Precise location, yes. At least in the US Navy this is an important part of the carrier's protection. (Having destroyers between the carrier and potential threats is another.)