The most efficient cartridge would be the one that has the largest diameter piston(bullet) with the longest stroke(barrel) from a chamber that had the densest fuel payload. I think a straight walled cartridge, and like
@AJC1 said not a hot one.
I like 45 Auto, I’ll go with that.
But if we didn’t waste energy out of the end, and the powder ceased putting pressure on the bullet as it exited, we’d need incredibly long barrels to get any kind of velocity outside of the barrel. But maybe no muzzle blast?
So, I’m more concerned with performance, not efficiency.
Super quiet, less than lethal rounds?
Or maybe...
In reality many cartridges are very efficient. The powder being burned and turned to plasma hot gases long before the bullet leave the bore. All of that pressure is captured and used while burning, just the “exhaust gas” is ejected.
Hmm, revolvers and their cylinder gap not withstanding perhaps.