hardhat-deploylets you easily verify contracts on Etherscan, and we have added a helper script to
/packages/hardhatto let you do that and we have abstracted the actual command away from the user. Please see the packages/hardhat/package.json and look for the 'verify' command, you will see the hardhat command in there (hardhat etherscan-verify --api-key <your_key>). You can pass the --network parameter.
yarn verify --network <network_of_choice>
Make sure to change the script so it uses your own Etherscan API key for the
"hardhat etherscan-verify --api-key <your_key>"
And all hardhat's deployed contracts with matching ABIs for that network will be automatically verified.