I just fixed this problem on my sink. The problem is actually a clogged filter in the quick connector under the sink. The quick connector is the black plastic part with the blue tabs (clearly visible in the 2nd video).
To remove the quick connector, simply squeeze the blue tabs and pull down. Then unscrew the other side of the quick connector to remove it entirely from the hose.
Using a small screwdriver, straw, etc, push the 2 white filters out of the quick connector. They can only be pushed out from one side, and take note of their orientation in the quick connector so you can put them back in correctly.
Once the filters are removed, you'll probably notice some debris in one or both of them. Sometimes it can be cleared by simply washing out the filters.
If needed, you can disassemble the filters to clean them. You don't need to remove the rubber O-ring. Using a small 2mm flathead screwdriver (or something similar), firmly press into the tiny groove on the side opposite of the O-ring, until you can wedge it in and pry the pieces apart. Once separated, the filter is easy to clean.
Reassemble everything in reverse order and test the water. It should be working again!
FYI this is a Glacier Bay sink, produced by Home Depot. If any of the parts have worn out (sometimes the O-rings do) or can't be repaired, take the quick connector to Home Depot and they might replace it under their limited lifetime warranty.