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/chatgpt/src/apply_command.rs

@@ -1,9 +1,9 @@
 use std::path::PathBuf;
 
 use clap::Parser;
-use codex_common::CliConfigOverrides;
-use codex_core::config::Config;
-use codex_core::config::ConfigOverrides;
+use llmx_common::CliConfigOverrides;
+use llmx_core::config::Config;
+use llmx_core::config::ConfigOverrides;
 
 use crate::chatgpt_token::init_chatgpt_token_from_auth;
 use crate::get_task::GetTaskResponse;
@@ -59,13 +59,13 @@ pub async fn apply_diff_from_task(
 
 async fn apply_diff(diff: &str, cwd: Option<PathBuf>) -> anyhow::Result<()> {
     let cwd = cwd.unwrap_or(std::env::current_dir().unwrap_or_else(|_| std::env::temp_dir()));
-    let req = codex_git::ApplyGitRequest {
+    let req = llmx_git::ApplyGitRequest {
         cwd,
         diff: diff.to_string(),
         revert: false,
         preflight: false,
     };
-    let res = codex_git::apply_git_patch(&req)?;
+    let res = llmx_git::apply_git_patch(&req)?;
     if res.exit_code != 0 {
         anyhow::bail!(
             "Git apply failed (applied={}, skipped={}, conflicts={})\nstdout:\n{}\nstderr:\n{}",