> Not really. It’s ground up and goes down the drain with the waste water.
It depends. What you describe is common with American dishwashers. European dishwashers typically don't grind anything up, they just collect it in a sieve.
If you buy a dishwasher with that feature. It's not standard. I know because my parents went cheap on their last dishwasher purchase because "they're all the same." About two years later I got to help troubleshoot why their dishwasher wouldn't get anything clean... the bottom of it was basically a solid layer of rotten food particles.
The Technology Connections YouTube channel has some nice, in-depth looks at dishwashers and soap.