This pic of a Tone class cruiser does seem to show side by side replenishment
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.