What is electrs:0.9.4

what is this electrs:0.9.4? newbie here

That is an electrum server which is a full node that allows electrum light clients to connect to it and verify transactions without storing the full chain. elects is basically a backend for light clients/mobile wallets.
Google is your friend.

I see around 15000 listening node (https://bitnodes.io/)
Is that include the electrum server node?

I would think so. If you klick on a country you can see all the available user agents that are advertised. This can just be changed in the bitcoind conf I believe.

I can’t find the electrs:0.9.4 in the list.

They must not advertise them there, not sure. You shouldn’t be concerned if you are.

What does it mean “verify transactions” ? Does that mean just look it up on the Mempool (in a secure way) ?

Look up ‘Simplified Payment Verification’ and ‘Light clients’ - A mobile wallet for example could run a light client. The wallet knows the transactions it is interested in but can’t check if a tx is included in a block since it’s not storing the block chain. Instead the wallet is connected to a electrum server which it can ask (Merkle proof) if a transaction was included in a block. That’s a messy and incomplete description of SPV but it conveys the gist I think. More on it here https://electrum.readthedocs.io/en/latest/faq.html#how-does-electrum-work

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