chore: update dependencies and examples

Cargo.lock changes:
- Update pulldown-cmark dependency
- Add markdown crate dependency
- Add lsp-types and ropey for input completion
- Add criterion for benchmarking
- Update all dependency versions

complete_integration.rs:
- Simplify example code
- Remove redundant initialization
- Improve error handling
- Add comprehensive documentation comments

Note: Dependency updates from new features added in previous commits:
- Markdown rendering (markdown crate)
- Input completion (lsp-types, ropey)
- Benchmarking (criterion)

Author: AlexMikhalev