Thw CleanJuice USB-C Battery Pack by RetroSix is drop-in replacement power board for your GameGear including USB-C connector and Lithium batteries.
Simply remove the old power board and replace it with the new one - the case does not need to be modified.
There's a switch where you can enable / disable the 34V (which are only needed if you still use the original LCD).
Instead of the barrel connector you will have a USB-C connector, so you can use any USB-C power supply to charge the included Lithium batteries. The batteries last much longer than the standard AA ones.
The batteries themselves are pretty much standard size, so you can easily get new ones in the future as well.