THE RN had tankers for side by side refuelling by mid war at least, until WW2 fueling at sea was not a priority as there were bases all round the world and astern feeling was regarded as sufficient. in the atlantic fuel for most ships was not a problem most of the time, the escort tasked old destroyers were modified with additional fuel and a tanker in Iceland provided additional fuel when needed. it was only in the Pacific when Japan expanded for supplies that an enemy appeared in an area that needed large amounts of refuelling. i think escorts were regularly refuelled alongside capital ships and carriers by 1942 at the latest after destroyers ran out of fuel during the Bismarck chase!
As for replenishment of avgas, ammunition, food, aircraft repair parts, and other supplies the IJN did complete 4 ships capable of directly supporting the fleet carriers. Two of the Sunosaki class and 2 of the Ashizuri class. Both classes were put in service in 1943. However, due to the acute shortage of tankers these ships were employed as oilers transporting oil from the former Dutch East Indies oil fields.
I believe when the Royal Navy (TF-37/57) was involved late in the war in the Pacific when using USN tankers to replenish they adapted the side by side technique.