Being able to stay at sea, without resupply, for longer than everyone else. This is a game changer. It transforms brown water navies into blue water navies and gives regional powers global reach. We can see it today; there are perhaps two countries capable of independently projecting top-tier power anywhere in the world for a sustained period (the US and France), with another few working on it (a few specific examples; the UK once it sorts out its naval air power again, China working on naval air power and in the last decade has transformed their logistical support navy to allow global deployment, Russia trying to become a serious naval power again, India ever advancing their naval ability). Some nations have tried and failed in recent years. To do it, you need a navy with global reach.
Technologies that were heavily improved in the years following WWII that massively improved the reach of warships:
Desalination.
Post WWII, the US put a lot of effort into desalination research. If you can make more freshwater, faster, for drinking, cooking, cleaning, cooling and freshwater-hungry maintenance tasks, you can extend the amount of time your ship can stay at sea without resupply. This extends the range of your ship, extends the logistic reach, just makes everything better. Ships that have to return to port every week are very limited in deployment; they need stronger logistics chains, they're more vulnerable to disruption, they need friendly ports, and so on.
Food preservation and compacting.
Similar advantages to being able to make freshwater. The more food you can carry, and the longer it lasts, the longer you can go without resupplying food. Freezer technology, preservatives, processing food to increase nutritional density. The technology of food preservation came on enormously in that time period.
Medical advances, and medical technology advances.
Crew get injured and sick. If you have to return an injured crew member to port, or transfer to another ship, it could be a very big deal. 207
The vessel may have to effectively take time out from its primary mission to meet a support vessel to transfer crew. Even if you don't do that, you're now a sailor short; you'd need to meet another ship or return to port anyway to replace that sailor, or continue at reduced capacity. The ability to keep your crew alive and healthy makes an enormous difference.
Also, communications. The ability to communicate quickly, reliable, securely and in large quantity with a vessel is genuinely transformative. Communications technologies came on enormously in the period in question. If you, and not your opponent, can talk to your warships anywhere in the world quickly and securely, and they can talk back to you, you have the advantage. You have a single consolidated view of everything your vessels are doing, what their condition is, what they can see. The closer to real-time you can make this information, the greater your advantage is. It's a huge advantage. If your opponent can only manage one short message a day, every one of his vessels has a delay on reporting, retasking, everything. It's the difference between a navy acting as a unified whole, and acting as fifty independent vessels doing their own thing. Wars get won and lost on communications. If you (and not your opponent) can coordinate your forces in near real-time, and you can disseminate information quickly throughout your forces, you can negate opposing force advantages in weapons, numerical superiority, speed, and so on. 500