Serbian term (edited): priključak / priključiti

this is most literally about the "connection point" between two pipes, nothing more complicated.

Whatever are these two pipes (water main, some local branch, whatever) it's about where they connect.


Connecting to the mains water supply
...
How to apply for a mains connection
Scottish Water are responsible for connections to the mains water supply.

..
https://www.mygov.scot/connect-mains-water-supply/

the same term applies to any other "connection" between two water pipes.

10 bara na priključcima unutrašnje hidrantske mreže
=
pressure of 10 bars at connection points with ...

it must be about the "connection point" and not any further point along the pipe / nor the whole pipe (be it a "branch" or whatever), as if there is any need to drop the pressure from 10 bars to 7 bars it would be done at the connection point between the two pipes.