Yea I'm not going to dox myself on this site, but having actually submitted papers and presented at various cryptography conferences and worked as an applied cryptographer in this field for 10 years, I think I have more cryptographic domain experience than some random furry-avatar security blog writer. Nobody recommends secp256*r1*. Nobody. The Koblitz curve is strictly better.
And libsecp256k1 as an implementation has received as much or more review by professional cryptographers (including many members of the well-respected Stanford cryptography group) than any other curve implementation, including many of the curve25519 libraries. It is battle-tested and very secure. There is, essentially, a giant billion-dollar bounty on the security of this curve and the correctness of its implementation. And in the history of cryptocurrency, there has never, not once, been a theft of money due to a cryptographic weakness or implementation error in this library. Unlike curve25519, whose non-unity cofactor for example was a source of inflation bugs in CryptoNote-based projects (e.g. Monero), something which secp256k1 mathematically prevents from being possible in the first place.
If you want to start a new project and not have to worry about potential cryptographic vulnerabilities with your choice of curve or algorithm, there are very few options to pick from. Both curve25519 and secp256k1 are pretty much the only two options, and they are pretty equal in terms of trustworthiness. If you are doing anything novel with publicly-visible digital signatures, I would absolutely recommend secp256k1 over curve25519 due to the cofactor situation.
And libsecp256k1 as an implementation has received as much or more review by professional cryptographers (including many members of the well-respected Stanford cryptography group) than any other curve implementation, including many of the curve25519 libraries. It is battle-tested and very secure. There is, essentially, a giant billion-dollar bounty on the security of this curve and the correctness of its implementation. And in the history of cryptocurrency, there has never, not once, been a theft of money due to a cryptographic weakness or implementation error in this library. Unlike curve25519, whose non-unity cofactor for example was a source of inflation bugs in CryptoNote-based projects (e.g. Monero), something which secp256k1 mathematically prevents from being possible in the first place.
If you want to start a new project and not have to worry about potential cryptographic vulnerabilities with your choice of curve or algorithm, there are very few options to pick from. Both curve25519 and secp256k1 are pretty much the only two options, and they are pretty equal in terms of trustworthiness. If you are doing anything novel with publicly-visible digital signatures, I would absolutely recommend secp256k1 over curve25519 due to the cofactor situation.