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/Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 edition = "2024"
-name = "codex-chatgpt"
+name = "llmx-chatgpt"
 version = { workspace = true }
 
 [lints]
@@ -9,12 +9,12 @@ workspace = true
 [dependencies]
 anyhow = { workspace = true }
 clap = { workspace = true, features = ["derive"] }
-codex-common = { workspace = true, features = ["cli"] }
-codex-core = { workspace = true }
+llmx-common = { workspace = true, features = ["cli"] }
+llmx-core = { workspace = true }
 serde = { workspace = true, features = ["derive"] }
 serde_json = { workspace = true }
 tokio = { workspace = true, features = ["full"] }
-codex-git = { workspace = true }
+llmx-git = { workspace = true }
 
 [dev-dependencies]
 tempfile = { workspace = true }