glue to the base

Por que no just fuse them together in your slicer and print as a monolithic part? You could probably even skip the base and just arrange the four bins together.

Being next to the sink, might be a good idea to drill drain holes into the bins so water doesn’t get trapped in the bottom. Otherwise pretty cool! Next gridfinity step would be making some kind of purpose built holder for the flosser picks and the toothbrush head.