Is a CMOS battery rechargeable? If so, what does its charger look like?
Most CMOS batteries are CR2032 lithium button cell batteries and are not rechargeable.
There are rechargeable batteries (e.g. ML2023) that are the same size, but they can't be charged by your computer.
Some motherboards used to have rechargable CMOS batteries on them.
In general now, no CMOS battery (especially the silver button cell type) are rechargable without investing in a specific rechargable version.
Do not - I repeat - DO NOT attempt to recharge a non-rechargable lithium cell (button type) as the resultant explosion and noxious gasses could kill you (or worse).