You can certainly buy third party batteries, but I personally only use Canon-branded ones. If you're going third party, be sure it's a trusted brand and you're purchasing from reliable sources.
In terms of a charger, the Canon branded one is Battery Charger CB-2LV.
I would advise against getting things from Amazon or eBay. As I wrote earlier, if going third-party, go with trusted businesses such as the various authorized Canon resellers (they have the more reputable third-party batteries/chargers).
I saw Wasabi batteries, which are one of the top aftermarket brands. Kastar is good too. When you're looking for a battery model this old, the options are limited from authorized Canon resellers.
09/26/2023: New firmware updates are available.
08/18/2023: Canon EOS R5 C training series is released.
07/31/2023: New firmware updates are available.
05/31/2023: New firmware updates are available.
05/18/2023: New firmware updates are available.
03/30/2023: New firmware updates are available.