Rename AuthMode to Backend, fix LiteLLM variant typo, add image update alerts, clean up Settings

- Fix serde deserialization error: TypeScript sent "lit_llm" but Rust expected "lite_llm"
- Rename AuthMode enum to Backend across Rust and TypeScript (with serde alias for backward compat)
- Add container image update checking via registry digest comparison
- Improve Settings page: fix image address display spacing, remove per-project auth section
- Update UI labels from "Auth" to "Backend" throughout

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

CLAUDE.md

@@ -72,7 +72,7 @@ docker exec stdout → tokio task → emit("terminal-output-{sessionId}") → li
   - `container.rs` — Container lifecycle (create, start, stop, remove, inspect)
   - `exec.rs` — PTY exec sessions with bidirectional stdin/stdout streaming
   - `image.rs` — Image build/pull with progress streaming
-- **`models/`** — Serde structs (`Project`, `AuthMode`, `BedrockConfig`, `OllamaConfig`, `LiteLlmConfig`, `ContainerInfo`, `AppSettings`). These define the IPC contract with the frontend.
+- **`models/`** — Serde structs (`Project`, `Backend`, `BedrockConfig`, `OllamaConfig`, `LiteLlmConfig`, `ContainerInfo`, `AppSettings`). These define the IPC contract with the frontend.
 - **`storage/`** — Persistence: `projects_store.rs` (JSON file with atomic writes), `secure.rs` (OS keychain via `keyring` crate), `settings_store.rs`
 
 ### Container (`container/`)