Pretty darn sure you have t remove the bumper, think they are bolted on behind.
Not very common for them to break but can be common this time of the year with the cold weather. Think they are hydraulic controlled and if they leak and water gets in, they can freeze, expand and break.
I could be wrong, but I thought all these VW group headlight washer systems were powered by a high pressure windscreen washer fluid pump, what happens is, the nozzles are closed while fully down and the pressure of the headlight washer pump lifts them up, the nozzle opens at the top end of its travel and releases the pressurised washer fluid, then collapses back down as the pump has stopped by now and the nozzle stalks have strong return springs to pull them back down, so maybe get that assembly out and see why it is weeping/leaking.
I'd make a silly reckless guess and say that there are probably seals in the stalk slides to keep the water in until the stalk is fully extended - and it is them that have failed, nice investigation job for when you get it off, I thought, but never needed to try on my old Passat B5, that it was possible to unbolt the washer from through the hole in the bumper - a lot easier probably to get the bumper off though, just needs the confidence to get round to doing it - I'll need to muster that inner "strength" when I get round to attempting a front parking sensor retro-fit!
Edit:- if/when you pull the stalk fully out, the washer fluid path will be open, so if there is any residual pressure in there it will dribble?