How can 22 awg cable over 100cm deliver 3A
My suspicion is that they've calculated the 3A capability based on the shortest cable they offer in that listing, which is 50cm. 0.5m of 22 AWG copper with 3A over it has a voltage drop of about 160mV, which is reasonable enough. At one meter, however, it's more like a 320mV, which is probably pushing it a bit if you're regulating 5.0V down to 3.3V with a linear regulator, because that reduces your headroom down from 1.7V to 1.38V.

However, if you know you're only ever going to run it at 1.7A max, you could probably get away with it. In that situation the drop would be more like 180mV (~3.6%) giving you about 4.8V to work with at the device, which should be fine for regulating down to 3.3V using an ESP32 board's onboard LDO.

Keep in mind that these are slightly conservative estimates that don't leave you much wiggle-room for operational variances, so I'd recommend trying to find a slightly thicker cable. Even 20 AWG would provide a marked reduction in losses, getting you closer to 100mV drop over a meter.