USB 2.0-only cables can't do PD negotiation, but they're USB 2.0-only anyway and cheap enough to just throw away if it's not what you want to have around (they're just regular old USB cables with different connectors soldered at their end).

Sorry, I meant data transfer+charging at the same time.

Every cable is suitable for at least USB 2.0 data transfer and 60W PD charging. Fully-featured cables get USB 3.0 data (at varying speed) and e-marked cables get >= 60W charging (100W or even higher with more recent PD revs). Thunderbolt (and USB4) has its own requirements.

If the above isn't true for your particular cable, it's either broken or what you're trying to do isn't specified by USB-C but rather some proprietary tech instead, in which case, blame your device vendor.

Interesting. I was testing this with a 4K USB-C monitor connected to MacBook Pro M1. Charging was not working due to "insufficient power".

I am trying to keep up with these spec details for a cable that is often marketed as just USB-C... it feels like an unnecessary cognitive load.

Unless you need to go above 60W, a cable does not have any way to influence negotiated charging profile at all.