Tagging a kiosk with additional logistics services (pick-up, drop-off etc)

Are these machines? If so see https://wiki.openstreetmap.org/wiki/Tag:amenity%3Dparcel_locker. If over-the-counter type services, I'm not so sure.

I'm still new to this so maybe I've misunderstood, but 1) that seems correct, but parcel lockers are often (always?) vendor exclusive, so a binary piece of information that a parcel locker exists isn't very helpful if you don't know what logistics company operates it, and 2) over-counter service is sometimes a thing also, sometimes vendors have only that option, sometimes they have both options at different premises (over-counter on one, then a box at another venue, or even outside). Perhaps it makes more sense to have the box as a completely separate object, so it can be outside, but if inside have a relation to the venue (much like an ATM?) -- and in case of over-counter it should be an amenity of the venue like amenity=servicepoint dhl or something?

Yes, map the box as a separate object. I'll be doing one soon located in the back of a shop.

do you have an example of what object type to choose, and how to specify operator?

this is the one I've just mapped: https://www.openstreetmap.org/node/9947325550