TL;DR: No, but they are much more vulnerable than they used to be, and the number of nations which can threaten them is increasing because the threats are getting cheaper to deploy.
You have two separate questions at work here, and I think we would benefit from disentangling them. They appear to be:
- Are aircraft carriers vulnerable?
- Are aircraft carriers useful?
Considering both of these questions might lead to a natural third question:
- Are aircraft carriers worth it?
Another thing we want to be specific about is: whose aircraft carriers? Most of the answers and possibly also the question implicitly assume the United States, but a US Navy aircraft carrier and anyone else's aircraft carrier are very different propositions.
Onto the first question: vulnerability.
Fundamentally yes; they are large warships and large warships can be sunk. Are they super vulnerable? No; they are very large warships, usually have better signal and detection capability, and have aircraft to use for defense. In the case of US Navy aircraft carriers, they are further surrounded by other large warships, each among the most powerful of their type. Why is this a conversation now and not thirty years ago? Because the stuff used to find and knock out large warships from land is now cheap enough that middle-weight countries can afford them.
Speaking to your specific example:
I.e. can’t an enemy send tons of cheap drone planes and drone submarines to first hunt for its location and then swarm-attack it?
Hypothetically yes. Now the question becomes: launched from where? If these are extremely long range drones, that comes at a premium - this is like electric car batteries, only more so. How to make sure the swarm is sufficiently intact to hurt the aircraft carrier when they get there? If you choose stealth, you have abandoned cheap, which makes a swarm very hard. How efficient are these drones in air-to-air combat against fighters? How vulnerable are they to anti-aircraft guns, and electronic countermeasures? If it is the US Navy again, we are talking about an organization that can put up kill ratios of 12:1 against peer aircraft. A modern carrier wing has ~40 strike fighters. Assuming drones much more capable than we currently deploy seems very reasonable, but 480 of them, plus accounting for other losses, plus the need to actually neutralize the carrier begins to seem like a complex challenge.
Onto the second question: utility.
A short review: aircraft carriers carry aircraft to sea. Their job is to bring these aircraft within range of the objective, and then the aircraft do the work they normally do (patrols, reconnaissance, stopping enemy fighters, bombing stuff). Then they can move to another objective.
Airpower is extremely useful, and control of the air makes everything easier for your side and everything harder for the other side, on land or sea. What does a better, or at least more efficient, job of providing airpower in naval engagements? The short version is that there are no replacements currently, and developing replacements introduces a series of tradeoffs and a very high cost.
Onto the final question: worth it?
There isn't, so far as I am aware, any plan which can replace the capabilities provided by aircraft carriers to the United States. This means we have to continue to pay, or go without. Another item to consider which is specific to the United States: the existence of our Carrier Groups is the bedrock assumption upon which the naval balance of power is calculated. This becomes significant when considering this question for other navies, which lack the experience, production support, strategic integration, and deep other fleet strengths.
My current opinion is probably yes for the United States, and probably no for all others.
Predictably, the problem is complex and there are many more dimensions to consider than I have presented, all in deeper detail. If you want to get a sense of how the discussion looks within the defense community, consider these sources:
Defense One, a popular defense news site.
War on the Rocks, long-form and more opinionated.
RAND, the military think tank par excellence.