docs: convert all patch.md examples from YAML to JSON

Updated all request and response bodies in the Patch documentation
(Merge Patch, JSON Patch, FHIRPath Patch) to use JSON format for
consistency with the rest of the API docs. Also fixed a typo
"BackboneElment" → "BackboneElement".

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

Author: vladzholnerchuk