It's way more complicated than that, but for the OP's purposes there are several levels of possible charging wattage, from "very slow" to "quite fast" and the devices will work at the level that they will all support. If you're having trouble sleeping here's the wiki page!but for practical purposes I think there are two levels that you are likely to encounter?
It's a device with a usb A plug, so i doubt it's a phone!
The original dumb USB A port could only deliver 2.5 watts. I think later enhancements allow 10 or 12 watts.
An appropriate USB C port can deliver well over 200 watts; the device has to request/negotiate this.
As for charging from a laptop when it's switched off, the "BIOS" is usually where you activate this capability.
It's not the USB A port which is the limiting factor, it's the version of the USB standard support by the chipset wired to the port.
A USB-3.1 compatible port would still take a USB-1.1 cable and provide the low power, but it could support up to 100 watts on the USB-PD (power delivery) standard if the cable and device being charged are compliant.