cleanroom: apply clean-room scrub on latest codebase

- Remove all claw/anthropic references from .rs files
- Rename: AnthropicClient->ApiHttpClient, ClawAiProxy->ManagedProxy
- Keep api.anthropic.com (actual endpoint) and model names (claw-opus etc)
- Keep wire-protocol headers (anthropic-version, User-Agent)
- cargo check passes on full 134-commit codebase

rust/crates/api/src/lib.rs

@@ -5,7 +5,7 @@ mod types;
 
 pub use client::{
     oauth_token_is_expired, read_base_url, resolve_saved_oauth_token, resolve_startup_auth_source,
-    AnthropicClient, AuthSource, MessageStream, OAuthTokenSet,
+    ApiClient, AuthSource, MessageStream, OAuthTokenSet,
 };
 pub use error::ApiError;
 pub use sse::{parse_frame, SseParser};