Phase 2: Rust Workspace Transformation (Part 1)

- Renamed directory: codex-backend-openapi-models -> llmx-backend-openapi-models
- Updated all Cargo.toml files:
  - Package names: codex-* -> llmx-*
  - Library names: codex_* -> llmx_*
  - Workspace dependencies updated
- Renamed Rust source files:
  - codex*.rs -> llmx*.rs (all modules)
  - codex_conversation -> llmx_conversation
  - codex_delegate -> llmx_delegate
  - codex_message_processor -> llmx_message_processor
  - codex_tool_* -> llmx_tool_*
- Updated all Rust imports:
  - use codex_* -> use llmx_*
  - mod codex* -> mod llmx*
- Updated environment variables in code:
  - CODEX_HOME -> LLMX_HOME
  - .codex -> .llmx paths
- Updated protocol crate lib name for proper linking

Note: Some compilation errors remain (type inference issues) but all
renaming is complete. Will fix compilation in next phase.

🤖 Generated with Claude Code

llmx-rs/core/tests/chat_completions_payload.rs

@@ -1,19 +1,19 @@
 use std::sync::Arc;
 
-use codex_app_server_protocol::AuthMode;
-use codex_core::ContentItem;
-use codex_core::LocalShellAction;
-use codex_core::LocalShellExecAction;
-use codex_core::LocalShellStatus;
-use codex_core::ModelClient;
-use codex_core::ModelProviderInfo;
-use codex_core::Prompt;
-use codex_core::ResponseItem;
-use codex_core::WireApi;
-use codex_core::spawn::CODEX_SANDBOX_NETWORK_DISABLED_ENV_VAR;
-use codex_otel::otel_event_manager::OtelEventManager;
-use codex_protocol::ConversationId;
-use codex_protocol::models::ReasoningItemContent;
+use llmx_app_server_protocol::AuthMode;
+use llmx_core::ContentItem;
+use llmx_core::LocalShellAction;
+use llmx_core::LocalShellExecAction;
+use llmx_core::LocalShellStatus;
+use llmx_core::ModelClient;
+use llmx_core::ModelProviderInfo;
+use llmx_core::Prompt;
+use llmx_core::ResponseItem;
+use llmx_core::WireApi;
+use llmx_core::spawn::CODEX_SANDBOX_NETWORK_DISABLED_ENV_VAR;
+use llmx_otel::otel_event_manager::OtelEventManager;
+use llmx_protocol::ConversationId;
+use llmx_protocol::models::ReasoningItemContent;
 use core_test_support::load_default_config_for_test;
 use futures::StreamExt;
 use serde_json::Value;
@@ -94,7 +94,7 @@ async fn run_request(input: Vec<ResponseItem>) -> Value {
         effort,
         summary,
         conversation_id,
-        codex_protocol::protocol::SessionSource::Exec,
+        llmx_protocol::protocol::SessionSource::Exec,
     );
 
     let mut prompt = Prompt::default();