When using an iOS device with a set of AirPods that have previously been paired, is the case also required whilst wearing them or can the buds be used without it?
No you don’t need the case to continue listening!
The case is only used for charging/storage and the initial (one time) pairing with your devices.
You can leave the case at home and get full usage out of the AirPods until the battery dies. This includes switching devices, monitoring battery levels, using Find My AirPods, etc.
I typically take the case with me unless I’m going for a quick jog/walk. I don’t recommend storing the AirPods anywhere other than the case or in your ears, to avoid losing them. Obviously the charging case prolongs the overall battery life as well.