Hi can't figure my electric water tank situation out and not sure if the contractor's/developers installed it correctly, since my neighbours have a different configuration.

Situation
I currently hear a low flow running water sound coming from the cold supply water valve that leads into the hot water tank. The cold water supply valve does have a drain outlet which they have attached some smaller piping and connectors to lead into the drain pan/hole below the tank (note my tank is upstairs). I currently see a slow flow of water coming out of this drain piping, which I believe is causing the issue. I believe after researching this issue, I have seen a few configurations where there is an expansion tank to keep the system closed, which I believe my system is currently not. However my neighbours have a small brass fitting that is between the cold water valve drain and the piping. Can my problem be that I am missing this fitting/device or are there other issues. Can anyone tell me what this fitting is perhaps.

Here are some pictures to give a visual


My Configuration - Sounds like low flow running water coming out of the valve drain
[drive.google.com]

My Neighbour's Configuration
[drive.google.com]

we don't do anything like this in the US ???

There are many types of sound that come out from water heater and every sound has its own cause like a humming sound is caused due to space between the looped tube is vertical to the tank. Electric water heater elements will make a cracking or popping sound when they become covered with sediment.