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/router.rs

@@ -12,10 +12,10 @@ use crate::tools::registry::ConfiguredToolSpec;
 use crate::tools::registry::ToolRegistry;
 use crate::tools::spec::ToolsConfig;
 use crate::tools::spec::build_specs;
-use codex_protocol::models::LocalShellAction;
-use codex_protocol::models::ResponseInputItem;
-use codex_protocol::models::ResponseItem;
-use codex_protocol::models::ShellToolCallParams;
+use llmx_protocol::models::LocalShellAction;
+use llmx_protocol::models::ResponseInputItem;
+use llmx_protocol::models::ResponseItem;
+use llmx_protocol::models::ShellToolCallParams;
 
 #[derive(Clone)]
 pub struct ToolCall {
@@ -178,7 +178,7 @@ impl ToolRouter {
         } else {
             ResponseInputItem::FunctionCallOutput {
                 call_id,
-                output: codex_protocol::models::FunctionCallOutputPayload {
+                output: llmx_protocol::models::FunctionCallOutputPayload {
                     content: message,
                     success: Some(false),
                     ..Default::default()