This will surprise you.
O1 tool steel is a chrome vanadium steel. In fact, it typically has more vanadium than A2. ( and less Chromium)
O1 also contains Tungsten , which A2 does not, so it also can be called a Tungsten steel.
Both of those elements work to limit the grain size of carbides, which is why you can get sharper edges with O1.
I doubt they are air hardening A2. First because the proper tempering is more complex, and because Paul has a video on prepping the chisels with emery paper. If it was A2 that would be difficult.
The steel probably isn’t O1, either. That’s an SAE designation. There are whole classes of similar metals with EU or Chinese designations.
Be wary of catch phrases. They don’t always tell you much.