- handlers.rs: add `uri` extractor to capture client's full path+query
- claude.rs: remove ?beta=true injection from build_url(), update tests
- stream_check.rs: remove ?beta=true from health check URL
The proxy no longer injects ?beta=true into API URLs. Instead, query
parameters sent by the Claude Code client are transparently passed through.
This fixes duplicate ?beta=true issues and aligns with upstream behavior
where the client already sends this parameter.