What is the procedure for handing over controller positions to the next shift?
I've asked an ATCO friend of mine who is in Greece in area control center and he told me is that there are no regulations; only good practices. For example, since for each sector you don't have one but two controllers, you don't change planner and radar operator at the same time. You might switch them 15 or 20 minutes apart. The supervisor is not involved in the process (there are several positions changing at the same time, who should they attend first?) and besides they are already busy with bigger things.

The current controller will need to brief the next one only if there is something unusual. Otherwise, the controller knows what sector they will take over and the sector peculiarities. Glancing at the current traffic will give them a good picture of what is going on. The relieved controller can stay next to the one who relieved them as long as they want but again, there is no time specified by regulations. But usually one or two minutes is enough. Usually an informal "Joe can I go? Need me anything else?" is enough and in the vast majority of cases the response will be affirmative.

This is specific for the Hellenic ACC, I don't know what happens in approach or tower positions although I have a feeling that things are not extremely different.