“If class is abolished in communism and the people are taken care of, why would anyone work at all? Who is going to work in coffee shops, pick up trash, work in stores etc.? What would be the incentive for people to do anything productive?”
Work still needs to happen. This takes coordination and organisation. Production is still required but people won't live in a class based society.
The modern world produces way more complicated things than a cup of coffee. People are still going to own personal possessions under communism. They just aren't going to be able to charge someone else rent to use their stuff.