@Tertius your example is expected behavior, coding it in a way to allow parallel pipes would be crazy complicated. (Probably easiest would be to give player straight not connecting pipe, right angle pipe, and T pipe, and let player to design it)
But my issue was that is was not really connected (my ...

As shown here the left pipe is empty and at same time claim to contain18k of water.
Until now I assumed that the two inputs are independent. But now it seems inconsistent, they are connected, but water does not go trough

oh thank you did not notice that, and I also did not know clicking on the pipe will show any information, including this in tutorial might be an useful for someone else who does not know this yet.
But also it is questionable if the water was actually in the system, because after you hint how it ...

I added new refinery and want to connect it to the other 2.
Connecting petroleun gas was ok, Light oil told me "Cannot connect systems with different fluids" :?: lets connect it last, because I did not see the issue, heavy old was ok.
I moved the connection point (last placed pipe) few times, to an ...