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/cloud-tasks-client/src/http.rs

@@ -13,8 +13,8 @@ use crate::api::TaskText;
 use chrono::DateTime;
 use chrono::Utc;
 
-use codex_backend_client as backend;
-use codex_backend_client::CodeTaskDetailsResponseExt;
+use llmx_backend_client as backend;
+use llmx_backend_client::CodeTaskDetailsResponseExt;
 
 #[derive(Clone)]
 pub struct HttpClient {
@@ -362,13 +362,13 @@ mod api {
                 });
             }
 
-            let req = codex_git::ApplyGitRequest {
+            let req = llmx_git::ApplyGitRequest {
                 cwd: std::env::current_dir().unwrap_or_else(|_| std::env::temp_dir()),
                 diff: diff.clone(),
                 revert: false,
                 preflight,
             };
-            let r = codex_git::apply_git_patch(&req)
+            let r = llmx_git::apply_git_patch(&req)
                 .map_err(|e| CloudTaskError::Io(format!("git apply failed to run: {e}")))?;
 
             let status = if r.exit_code == 0 {