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/src/tools/handlers/mcp.rs

@@ -52,11 +52,11 @@ impl ToolHandler for McpHandler {
         .await;
 
         match response {
-            codex_protocol::models::ResponseInputItem::McpToolCallOutput { result, .. } => {
+            llmx_protocol::models::ResponseInputItem::McpToolCallOutput { result, .. } => {
                 Ok(ToolOutput::Mcp { result })
             }
-            codex_protocol::models::ResponseInputItem::FunctionCallOutput { output, .. } => {
-                let codex_protocol::models::FunctionCallOutputPayload {
+            llmx_protocol::models::ResponseInputItem::FunctionCallOutput { output, .. } => {
+                let llmx_protocol::models::FunctionCallOutputPayload {
                     content,
                     content_items,
                     success,