List of games with battery backup:

https://segaretro.org/Battery_backup

As for the Japanese carts, you can use a heat gun on the rear label to soften the glue and easily peel back the label to access the screws.

I've personally never seen a Genesis battery leak, but I've replaced a handful of dead ones. They all use the same 3V 2032 cell. The listing I bought form is gone, but here's one that's the same: https://www.amazon.com/dp/B095P2THNR/

Do not get rechargeable ones. All games use single-use batteries.

Not that I've tried it myself, but if you wanted to be creative, you could also try to put in a socket to make future replacements easier: https://www.amazon.com/dp/B071F3HW8J/