Water from the tap seems to be soaping up(??)

Despite experiencing this since I've moved into this appartment, I only realized today that the water from the bathroom sink seems pretty soapy... I've always chalked it up to weird behavior of hard water, but now I'm a bit concerned...

I excessively wash my hands and so I used soap like 10 times during cleaning, which filled the sink with soap. I let the water run, but I noticed that when I held my hands in a cup shape and let the "hand cup" be filled with water, the water would be very bubbly. I would rub my (clean and washed) hands together and it made my hands soapy. I thought maybe it's just residue of the soap on my hands, so I just washed all the bubbles down the drain and went to immediately take a shower.

In the shower I noticed there was absolutely no bubbling up of the water, and after washing, I went to the bathroom sink again, held my hands under water (which was again bubbling), rubbed them together, and hold and behold, soapy residue. I let the sink run for a couple minutes and then it stopped bubbling and soaping.

What's the problem and why is this happening? I was drinking water from this sink for years and now I'm wondering if I've been poisoning myself with soap.