Is it generally possible to convert a drivetrain on a bike from a chain to belt drive? What exactly is involved with this task?
Generally no, for the simple reason that unlike chains belts are continuous and can't be split, so belt drive bikes need a split chain or seat stay, or a removable dropout.
If you had a single speed or internally geared hub chain drive bike with a removable dropout, at a minimum the rear sprocket, chainring and chain would have to be replaced.
Traditionally you would need a split in the rear triangle to fit a belt drive.
There is a company named Veer that offers a split belt for with supporting sprockets for several internal hubs such as Rohloff and Shimano Alfine. https://www.veercycle.com/collections/all/products/split-belt-pro
With a belt drive you will need an internal hub or go single speed.