Having checked 2 main NEAR explorers, the official one and nearscan, I haven't found neither any way to see the byte code and source code of smart contracts on them, nor ability to interract with a smart contract, nor check what functions a smart contract has. On any Ethereum Explorer, and on a few others, all of this is possible.
Or perhaps I've missed something?
Is it correct that on NEAR explorers neither of the abovementioned features exist?
very good question.
You can use "Stats Gallery", this tool let you see Stats from an account (Or contract - which is an account with a contract deployed).
But let you interact with the Contract too.
https://stats.gallery/mainnet/nit.globaledu.near/contract?t=week
This is an example, you can see the functions of my "Feedback Contract". Instead of this you can add a Testnet contract and try to call some functions, maybe the next one:
https://stats.gallery/testnet/alpha.neatar.testnet/contract?t=week
And the source code of the tool is here, just in case you want to know exactly how is does:
Saludos