Changing prop name from UI doesn’t change prop name at backend

Please provide the corresponding Component config entity at each stage. Specifically, any change to the code component that is *saved* (not auto-saved, but actually saved) SHOULD result in an update to the code component's Component config entity.

(That would be experience_builder.component.js.[machine name of code component].)

Export it either using drush cget or at /admin/config/development/configuration/single/export

Remove component from page and then from components list

This is very hard to interpret. I think the first time "component" really means "component instance", and the second time you're removing the code component from

Please always use the term "component instance" when referring to an instantiation of any component (no matter whether it's an SDC, code component or block plugin).
"component" refers to the generic concept that can be instantiated, represented inside XB itself by the Component config entity — which is how XB knows about a component coming from some source (SDC is a source, code components are a source, block plugins are a source).