Re: How many battery "breakthroughs" is that this year?
Well, for EVs at least (and given the commonality of technology, most other Lithium battery uses as well) the last 7 years has seen about 5x reduction in $/kwh cost and maybe 3x increase in kwh/unit volume.
Exactly what has made this possible is only really known to the battery manufacturers, and I doubt they want to discuss it much. It's most likely a combination of a few step changes (although not on the "3x better" scale) and lots of little tweaks.
Most technologies don't usually experience huge overnight jumps, but if you wait a few years and look back--. Look at semiconductors for instance.