As you say, batteries have been around for a long time. The rapid growth/improvement part of the battery curve happened back in the late 1800s/early 1900s.
The lead-acid grid lattice design, still the...errr...gold standard when it comes to the most amount of joules stored per buck, was invented in 1881.
(modern technologies like the various lithium battery chemistries win when it come to storage for a given mass -- thus their use in things like portable devices and cars, but lead-acid still wins when it comes to storage for a given cost).
Li-ion has caught up. If you have $400 to spend on batteries both li-ion [1] and comparable lead acid [2] (deep discharge, long cycle life) cost around 3 Wh/$.
[1] https://www.imrbatteries.com/samsung-29e-18650-2850mah-2-75a...
[2] https://www.powerstream.com/BBep.htm (EP100-12)
We also have lots of different designs to experiment with, and much better computers for running simulations. As the computers improve, fusion progress will speed up, if the funding is available.
* (The triple product of temperature, density, and confinement time is the critical fusion metric; for every fusion fuel there's a triple product above which you get net power.)
Nothing resembling Moore’s law style advancement, despite a lot of money to be made.
It is likely exaggerated but the headlines claimed the big Australian battery returned the investment within a couple of months. There’s a LOT of money to be made on energy storage.
Why would fusion reactors be moorable?