Libsecp256k1 is designed to work on embedded systems too– and AFAIK it’s the only publicly available library with any power analysis countermeasures at all, but like other generic embedded libraries you need to configure it for its usage.
There should be a document that describes how to configure and build the library for embedded use and helps people avoid obvious pitfalls (e.g. mistaking the extensive tests as something that needs to go on the embedded device, missing the functions you’re supposed to replace with your own implementations).