I think in a recycling scenario you’re gonna be stripping these batteries down to their cells anyway, so their physical format is kinda irrelevant.
As for their properties, you’re almost certainly better of just measuring them, rather than relying on some sort of digital spec sheet. You’ll have no idea what life these batteries have led, and thus no idea how much they’ve drifted from their spec sheet.
The battery chemistry pretty much determines all their important characteristics such as voltage, and charge/discharge pattens. There’s a very limited number of fundamental battery chemistries to pick from, and you can almost certainly ignore the secret source car manufactures are using. You just end up running the batteries slightly less efficiently, but again their at the end of their automotive life, which is the bit when people actually care about peak efficiency.
As for you analogy, it’s a bit more like wheels and tires on a car. There are hundreds of different tire treads, and plenty of different wheel sizes. But if you’re recycling a wheel or tire, you almost certainly don’t care much about either it’s size or tire tread, because it’s trivial to build a recycling process that can handle almost any type of wheel or tire.