Do you think, with modern sensors and so on, they could have a lot of that maintenance of tension stuff managed by a smart computer system with some human oversight? (To reduce crew required?)
What would they call it? UNREP - that could work. RAS not so much (but RIS could - Replenishment In Space.... I suppose RAS could be Replenishment Along Side).
I'm imagining:
An framed collapsible umbilical corridor with a built in clips and an electric (or manual) winch system (or mag accelerator/decelerator). That could move containerized stuff and people.
A separate umbilical (perhaps an unfolding automatic boom) that will handle the fuel.
Or would you try to go lock-to-lock?
If you planned on doing this kind of thing, your ship could have a big belly lock and the replenishment vessel could have same and you could hard dock those standard locks (belly to belly) and then your fuel transfer could even be from hard lines via a coupler so no hoses that could get torn.
Depends how fast you wanted to breakaway.
Certainly for ships being refilled by ships not in their fleet or that are civilian ships or some sort of multi-nation flotilla, you might still need the classic UNREP vs a hard dock.
I know during Katrina, Lt. Cdr. P. Pournelle's vessel (Jervis Bay trimaran on loan from Oz, thus oddly could not be called USS anything) did vertical reps with choppers, accepted cargo from piers, accepted cargo lowered from carriers, and did other replenishing moves (perhaps a classic side-by-side UNREP) when at sea. And the fact the vessel had low draught meant it had less chance of fouling and could go up rivers. Those vessels are pretty neat for unarmed (or lightly armed) naval cargo vessels. And fast too. I think they did New Orleans to Galveston and back in maybe 10 hours including loading up.