I was not even aware there was a v2. I examined the one that came with my (used) A7Riii and see no version number anywhere, but perhaps it is the original version. It could have something to do a tweak for the new models that have been introduced since v2, but that is a complete guess.
Since the part number is the same, and they have to maintain compatibility, I am going to guess there are only very minor differences between versions that are not apparent to the user. Unless the manual for your particular camera mentions needing a particular version, it likely does not matter. Purchase the v3 if it is an option, but I personally would not worry at all about purchasing a v2 battery.