refactor(provider): switch from full config overwrite to partial key-field merging

Replace the provider switching mechanism for Claude/Codex/Gemini from
full settings_config overwrite to partial key-field replacement, preserving
user's non-provider settings (plugins, MCP, permissions, etc.) across switches.

- Add write_live_partial() with per-app implementations for Claude (JSON env
  merge), Codex (auth replace + TOML partial merge), and Gemini (env merge)
- Add backfill_key_fields() to extract only provider-specific fields when
  saving live config back to provider entries
- Update switch_normal, sync_current_to_live, add, update to use partial merge
- Remove common config snippet feature for Claude/Codex/Gemini (no longer
  needed with partial merging); preserve OMO common config
- Delete 6 frontend files (3 components + 3 hooks), clean up 11 modified files
- Remove backend extract_common_config_* methods, 3 Tauri commands,
  CommonConfigSnippets struct, and related migration code
- Update integration tests to validate key-field-only backfill behavior

src-tauri/tests/provider_service.rs

@@ -414,9 +414,19 @@ fn provider_service_switch_claude_updates_live_and_state() {
     let legacy_provider = providers
         .get("old-provider")
         .expect("legacy provider still exists");
+    // With partial merge backfill, only key fields are extracted from live config
     assert_eq!(
-        legacy_provider.settings_config, legacy_live,
-        "previous provider should receive backfilled live config"
+        legacy_provider
+            .settings_config
+            .get("env")
+            .and_then(|env| env.get("ANTHROPIC_API_KEY"))
+            .and_then(|key| key.as_str()),
+        Some("legacy-key"),
+        "previous provider should receive backfilled auth key"
+    );
+    assert!(
+        legacy_provider.settings_config.get("workspace").is_none(),
+        "backfill should NOT include non-key fields like workspace"
     );
 }