Brownie cant verify the contract on etherscan

Short answer is: you have to create the API key at etherscan.io either for the mainnet and the rest of public testnets (Ropsten, Rinkeby, Goerli..).

(Bonus)

In addition, I had some issues when trying to verify a contract with interfaces located in subdirectories.

Perhaps it is not your case, but if you are using Truffle to manage the contracts deployment, there is an interesting plug-in to verify the contract automatically: truffle-plugin-verify.

I tried it and it worked perfectly. You essentially need to

• Install the truffle & plugin via npm
• Create an API key on Etherscan
• Update the truffle configuration file
• Use a wallet to sign the transaction to create the contract (e.g.: @truffle/hdwallet-provider)
• Migrate, and finally, verify the contract

Since you can't access internal or private functions externally for both contracts and libraries I wrapped the method/s of the library SimpleMath in the method/s of a contract called TestSimpleMath, which has it's methods set to external, thus exposing the library method/s.

import { SimpleMath } from '.SimpleMath.sol';

contract TestSimpleMath {
  function add(uint a, uint b) external pure returns(uint) {
    return SimpleMath.add(a, b);
  }
}