Batteries are not good in terms off energy density compared to fuel. You would not carry as much fuel as a conventional ship, maybe 1/3 or 1/4. That can also cover helo operations and backup genset power.
You are quite right but if large sections of the ship can be closed off and filled with hydrogen gas then fuel cells can act as batteries with better fuel efficiency than a motor... a cryogenic section could be used to liquefy the hydrogen... the pure oxygen could be vented or burned with LNG for cooking or heating the ship in cold places...
It just seems so weird that the russians would cancel all plans to build a nuclear cruiser when they have enough reactors, state of the art off the shelf weapons and sensors, as well as near future free spots in shipyards.
Who said anything about cancelling plans?
They have access to rather more information than we have available to us... for all we know in 10 years time they might have plans for a totally new type of power system that is powerful and compact and reliable and not as expensive as current options...
There might be radar technologies that are on the way that will make current radars and stealth technology redundant and silly.
They are at the start of developing an all electric drive ship... some of the technologies involved might make serious changes to the way ships are designed and built... what they really need to do is start producing corvettes and frigates in useful numbers so older model vessels can be retired, and they need to start on a destroyer class to support the new helicopter carriers that are on the way.
They currently have a few cruisers... ex Kirov and ex Slava class ships that are not amazing... are not best of class in the world... but can sail around the world and do things cruisers are supposed to do...