Added search settings controller, sync settings in popup with the class

src/lib/extension/settings/SearchSettings.js

@@ -0,0 +1,42 @@
+import CacheableSettings from "$lib/extension/base/CacheableSettings.js";
+
+export default class SearchSettings extends CacheableSettings {
+  constructor() {
+    super("search");
+  }
+
+  async resolvePropertiesSuggestionsEnabled() {
+    return this._resolveSetting("suggestProperties", false);
+  }
+
+  async resolvePropertiesSuggestionsPosition() {
+    return this._resolveSetting("suggestPropertiesPosition", "start");
+  }
+
+  async setPropertiesSuggestions(isEnabled) {
+    return this._writeSetting("suggestProperties", isEnabled);
+  }
+
+  async setPropertiesSuggestionsPosition(position) {
+    return this._writeSetting("suggestPropertiesPosition", position);
+  }
+
+  /**
+   * @param {function(SearchSettingsObject): void} callback
+   * @return {function(): void}
+   */
+  subscribe(callback) {
+    return super.subscribe(rawSettings => {
+      callback({
+        suggestProperties: rawSettings.suggestProperties ?? false,
+        suggestPropertiesPosition: rawSettings.suggestPropertiesPosition ?? "start",
+      });
+    });
+  }
+}
+
+/**
+ * @typedef {Object} SearchSettingsObject
+ * @property {boolean} suggestProperties
+ * @property {"start"|"end"} suggestPropertiesPosition
+ */