How to use USB-C cable with a charger
There are few caveats in your project. First, if the Anker charger is true Type-C charger, it won't output VBUS until it will see 5.1k pull-down from your Type-C receptacle. So you must provide two pull downs, on CC1 and CC2 pins, before you will see any power.

Second, as soon as you signal to the charger that some consumer is connected, the charger will output VBUS, but it is your device responsibility to limit its intake to 3 A. Since you will have three devices downwards, and each device might take 1.5 to 3 A each, you might be running into overload, or some odd unstable behavior. So this would be your nightstand responsibility to provide charging signatures to your devices such that they don't take total more than 3A. Usual smartphones can customary take 1.5A, so there will be troubles if all three would start charging at max rate.

The easiest way to limit consumption is "no signature" on downstream ports, when D+/D- are floating, not connected. Then some devices will understand this as a standard USB port, and will limit their consumption to 500 mA. This is obviously not very optimal, and some phones might refuse the input at all. For better charging experience the multi-port charger must have some intelligence, which is a fairly broad topic.

Third, a Type-C receptacle is a very tiny device with pin pitch of 0.5 mm. It will be quite challenging just to attach wires to it, usually it requires a fine PCB with proper fan-out.