(Non-antibacterial) soap just sticks to bacteria, making them more slippery, so they can be washed away. They're still alive in the drain and septic/sewer.

But soap doesn't just magically do this - it has to be foaming, as scrubbing allows the soap molecules to magnetically organize. As the hydrophobic soap molecules stick to the non-polar bacteria, they form a bubble shell that's not unlike a cell wall. To produce this foam with normal hand soap takes ~20 seconds of rotational scrubbing - a soap-Rasengan, if you will.

Bacteria are in everything, including every breath of air and gulp of water. Our immune system kills the ones which get through our small intestine's mesh system.

Soap doesn't kill germs, it simply makes it easier to wash germs off by making water fit into smaller areas.

So, a damp sponge is a perfect environment for growing bacteria.

Now if you are using antibacterial soap your sponge may be fine like that, but then those soaps have concerns of their own (eg. They kill good bacteria that we apparently want to keep around)

Soap is mostly for helping to remove dirt by helping both scrubbing and the mixture of oils in water. I think it has some side-effect as an antibacterial due to pH or something, but it's not inherently a bug killer (of course, you can get anti-bacterial soap these days. Arguably a bad thing globally).