I'm not sure a carrier strike group would actually outright lose to a giant swarm of drones, at least in terms of the carrier being sunk. A Shahed warhead is pretty small once you're using it against large warships.
That said, I wonder why you don't see Ukraine and Russia doing this more -- "saving up" for massive clouds of long range strike drones every couple weeks, instead of sending out a couple hundred every night. It feels like the latter strategy would be more effective, saturating air defenses and what have you, but it doesn't seem to be used much. Maybe launching that many drones at roughly the same time is really hard?
I suppose there is an opportunity cost to saving up all your weapons. What is the enemy doing in that time where you stop throwing things at them?
Otherwise, what stopped them from saving up all the bullets, artillery, or bombs and sending them out in brief pulses in prior wars...
A carrier is nearly impossible to sink. However, a bunch of flaming jet fuel sloshing around a big bathtub with thousands of americans on it is effectively as disastrous.
I don't think they are fully automated in Ukraine vs Russia. For an onslaught you'd need to either have a lot of pilots, full automation or some in between of like 1 pilot controls one drone but another set of 10 drones fly in formation with the pilot and will self destruct hitting the same target the pilot flew into, but I'm not sure software for this exists yet.