feat(provider): use live config for edit and backfill SSOT after switch

- Edit modal (Claude+Codex): when editing the current provider, initialize form from live files (Claude: ~/.claude/settings.json; Codex: ~/.codex/auth.json + ~/.codex/config.toml) instead of SSOT.
- Switch (Claude): after writing live settings.json for the target provider, read it back and update the provider’s SSOT to match live.
- Switch (Codex): keep MCP sync to config.toml, then read back TOML and update the target provider’s SSOT (preserves mcp.servers/mcp_servers schema).
- Add Tauri command read_live_provider_settings for both apps, register handler, and expose window.api.getLiveProviderSettings.
- Types updated accordingly; cargo check and pnpm typecheck pass.

src-tauri/src/lib.rs

@@ -415,6 +415,7 @@ pub fn run() {
             commands::open_external,
             commands::get_app_config_path,
             commands::open_app_config_folder,
+            commands::read_live_provider_settings,
             commands::get_settings,
             commands::save_settings,
             commands::check_for_updates,