The battery in my Japanese built Toyota is from GSYUASA and is made in Japan. Its been a very good battery.
The last time I saw a Yuasa car battery was the OEM one in the 1989 Integra that got me through college. That was a classic design with flush top caps that needed a wide screwdriver to remove and secure. Later cars I got that were assembled in Japan had Panasonic batteries with knobbed caps.
I don't know of anyone who still sells that style of battery in the United States. When I was thinking of getting a BRZ that might have been sitting on the lot for a while (we had a hard time finding one that would start on the lot to test drive) I was thinking maybe if I bought one to ask for a new battery. However, having the factory installed battery with caps sounded like a good idea. Their replacement batteries were all the kind of with ganged caps or perhaps glued on caps.