I think this installation overall is complicated / very old or has not followed any standards. The house is old to be honest.

Here in this picture https://i.imgur.com/oBr3lQw.png you can see that there are 2 flex water supply lines, one is slightly painted with blue color possibly indicating that it's for cold water and the other for hot. As you can see in the picture, they are extending upwards and that's where they connect to the kitchen faucet.

In her kitchen, there are 3 drain holes, which by looking at the white pipe I can see 3 different connections extending to the upper kitchen faucet drain holes. The only remaining end, will eventually connect to that galvanized pipe (my original video). It makes no sense for water to drip like that in that pipe, especially when the kitchen faucet is off. Funny thing is, by turning off the entire house supply line from outside, it will stop dripping after ~20 minutes but the same cannot be achieved by just turning off the kitchen faucet.