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It's all that funky press-fit shit on the coffee machine side of things. It goes from mains into splitter, with the coffee machine feed going into a water filter system via (some guys name) press fit.
It was 7 years ago. I'll have to google it to find out where to find the fitting. Or might see if I can just replace the O-ring in it if need be. Pain in the arse as I have to keep moving the washing machine to get to it.
Plumbing woes, obviously it should all work without much bodging but you might have an issue with the pipe from the coffee machine. Occasionally the ends of plastic pipes which press onto an O ring or other plastic fitting get marred or damaged by fitting issues, then when you change the fitting for a new one the old damaged end won't seal. It's usually a bitch to spot because the plastic looks fine with a cursory inspection but a small deformation or mar in the end can cause water under high pressure to leak out.
tl:dr Change the pipe to the coffee machine. You may need to change your new fitting too as the end of the coffee machine pipe might have damaged it.