Now, both class societies in the Maritime Battery Forum have rules for energy storage on ships. DNV GL has had energy storage in the rules for some time (access here) and now BV has released theirs.
"With a growing number of hybrid vessels entering service, Bureau Veritas has recently released a new series of notations and rules addressing the requirements of energy storage systems (ESS) to support ship operators in reducing emissions." You can access the full news article from the the BV homepage here.
The BV rules can be found in Pt F, Ch 11, Sec 22.
The DNV GL rules for energy storage systems are found in DNV GL rules for classification: Ships (RU-SHIPS) Part 6 ch. 2, section 1.