The vast majority of C to C "charge" cables are USB 2 cables. I don't believe I have ever received or even seen a "charge only" non-captive C to C cable. A to C cables are a lot more common.
Do you have reason to believe that the C to C cables you got/bought don't support USB 2?
It doesn't make sense for a random accessory to come with a charge only C to C cable because USB 2 C to C cables are a dime a dozen. They're almost certainly paying more money to produce a spec violating cable.
They could have data support, I've never actually checked. The wires are pretty thin so I only trust them for charging the lights they came with. I have a bundle of similar looking A to mini or micro B cables of which I know many are charge-only. As long as they're super short I only rely on them being useful for charging.
In that case they almost certainly do have data support.
Keep in mind that power dissipation scales with the square of the current. That means that, as a first order approximation, relative to household 15 amp wiring, a 3 amp cable can be 1/25 of the size. You can get away with really thin wires for that.
The reason why you end up with thick USB C cables is because of either 5 amp support (requiring 2.8x bigger wires) and/or USB 3 support (requiring a bunch of extra higher spec wires). It is quite normal for plain old 3 amp USB 2 USB C cables to be thin.
I'm curious, next time I'm charging devices I'll check. Either way they're still not useful for anything beyond accessory charging, they're short and won't carry the power+signal necessary for my laptop (which, sigh, has two kinds of cables because the one Apple provided with their charger won't do Thunderbolt).
Do you have reason to believe that the C to C cables you got/bought don't support USB 2?
It doesn't make sense for a random accessory to come with a charge only C to C cable because USB 2 C to C cables are a dime a dozen. They're almost certainly paying more money to produce a spec violating cable.