Widget persistence API

Instead of persisting widgets ourselves, this PR provides the tools to allow users to persist widget states however they want.

This PR also includes some bugfixes, one of which is the removal of views on cell re-execution!!!
Based on #6664 

- [x] Try it
- [ ] Include examples
- [ ] Include tests

@ellisonbg @SylvainCorlay @jasongrout 
Okay, I cleaned up the logic so it looks nicer and makes sense.