Add GitHub private-repo sync (token-based) for notes, chats and diagrams

[nigussolomon]

Motivation

• Provide a simple, token-based mechanism to sync selected items (notes, chats, diagrams) to a user-owned private GitHub repository.
• Allow creating the private repo automatically and pushing the current local InkCaliber content for a specific item on-demand.

Description

• Added a Tauri command sync_to_github (apps/inkcaliber-desk/src-tauri/src/lib.rs) that verifies the PAT by resolving the GitHub user, ensures a private repo exists (creates it if necessary), initializes/updates a local git repo under Documents/InkCaliber, commits, and pushes using token-based auth headers.
• Added a frontend service apps/inkcaliber-desk/src/services/github-sync.ts that prompts for a Personal Access Token and repo name on first use, stores the config in localStorage, invokes the backend sync_to_github command, and clears stored config on auth failures.
• Wired the UI sync indicator in the active editors to trigger per-item syncs by calling the service with the correct item path (notes/<name>.json, chat/<provider>/<name>.json, diagrams/<session>/<branch>.excalidraw).
• Performed small TS cleanups to remove unused imports/refs so the frontend build succeeds.

Testing

• Built the frontend with cd apps/inkcaliber-desk && npm run build, which completed successfully.
• Attempted to run cd apps/inkcaliber-desk/src-tauri && cargo check, which failed to resolve crates due to blocked access to crates.io in the current environment (network restriction), so Rust binary validation could not be completed.
• Verified the TypeScript changes and removal of unused symbols to resolve initial tsc errors and allow the frontend build to finish.

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Codex Task