A quick and easy way to “get rid of” or “do away with” or “solve the problem with” the tiny bits of soap bar pieces and remains that you are left with in the shower is to stick it to a new bar of soap. The trick is knowing when to do this. Should you do it at the start of a shower, during a shower, or after a shower? The answer is to do it after a shower because the soap bar remains will have time to dry onto the new bar of soap without the presence of running water. If you do it at the start of a shower, the remains will not be able to stick to the new bar of soap due to all the running water.
If you tried this in the past, and it did not work, then this may have been the reason, an issue of timing.
For the sink, just get the new bar of soap and the left over pieces wet. Then let the new combo sit overnight.
If you devote the time, you can do it the hard way.
If you do activities like this, you may be a resource conscious person like me.