Update docs and example spec to use new directory structure for azure-rest-api-specs

- [ ] Update typespec-azure website to indicate the new directory structure
- [ ] Update the contosowidgetmanager sample to use the new directory structure
- [ ] Ensure that the appropriate init feeds are compliant with the new structure

Locate the typespec-azure website content, the contosowidgetmanager sample, and the relevant init feeds, then compare their paths with the new azure-rest-api-specs directory structure. Update the website and sample references and verify that all appropriate init feeds comply with the new structure.

Written by the indexing model from the issue text.