fix(extension): badge clear must use a valid color, not empty string

Follow-up to 6e5f82a — that commit's edit to background/index.ts was
lost. Apply the actual fix: replace setBadge("", "") with
setBadge("", "#00000000") so Chrome's setBadgeBackgroundColor doesn't
throw "The color specification could not be parsed."

Co-Authored-By: Claude Opus 4.7 (1M context) <[email protected]>

Author: jt55401

src/background/index.ts

@@ -750,11 +750,14 @@ async function updateBadge(): Promise<void> {
     // Get the verification status for the current URL
     const status = await getVerificationStatus(currentTab.url);
 
-    // Set the badge based on the verification status
+    // Set the badge based on the verification status. Clearing the badge
+    // means setting text to empty; color must still be a valid color string
+    // because Chrome rejects an empty color spec ("The color specification
+    // could not be parsed").
     if (status.verified) {
       await platformAdapter.setBadge("✓", "#4CAF50");
     } else {
-      await platformAdapter.setBadge("", "");
+      await platformAdapter.setBadge("", "#00000000");
     }
   } catch (error) {
     console.error("Failed to update badge:", error);