No I shouldn't have to visit an external website if I am running a full node. That should be the point of running blockchain. I am sorry but bitcoin-cli has simpler commands. Just run a listreceivedbyaddress and it shows you txids, confirmations, everything!!
Ethereum is intentionally convoluted and unfriendly TO MAKE people depend on websites like etherscan. That is criminal and bad politics to maintain control.
Anyone running a full blockchain should be able to track down details of their address with simple commands.
On ETH one has to go through details of every block to find a needle in a haystack. There is no direct way to find txids associated with your own address. I am sorry but that's the hard fact. Having to depend on an external website to get details about your transaction defeats the purpose of decentralization!

I am running a full node. I have an ethereum address. I am expecting some ETH to be deposited. No idea who the sender is. I can see it's arriving. balance has changed. I want to know the txid. What command do I fire?

bitcoin has simple commands to get confirmations and txid. How do I do that in ethereum. I am not asking for much just want to know the txid using geth or RPC !! Kindly advise.