I had a basin yesterday that took ages to drain.The slot was covered with silicone.
Can you slide a piece of wire from the basin overflow down to where the waste fits. A vacuum seems to be the only thing you haven't ruled out although with waste plug open I don't really see how one could formFunnily enough, I did think that maybe I'd obscured the slot (my first attempt I didn't realise the slot was a thing - I've not done a basin before!) but part of my second attempt was checking it was all clear and lined up correctly. I'd had the idea that if the overflow couldn't allow air in, then it would perhaps make a vacuum, which would stop it draining.
Alignment isn't critical if the basin moulding has reasonable annular clearance around the slot area.I didn't have the waste aligned with the overflow at first (the instructions don't tell you!)

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