Recommendations for original iPod battery replacement

Not Apple. They won't have the parts any longer.

We have no idea where in the world you are located and you can probably do a general web search as easily as we can. I suspect it may be very difficult to find one given that that is a 22 year old piece of technology.

Remember that batteries are little factories that convert chemical energy to electrical energy. The raw materials they store for use degrade over time. If offered a "original" Apple battery, it is surely far beyond its sell-by date and is probably seriously dead after almost two decades.

Caveat emptor!