fix: default backlinks search to site-wide scope for root URLs (#96)

* fix: default backlinks search to site-wide scope for root URLs

URLs with an explicit protocol but no path (e.g. https://example.com/)
were incorrectly auto-selecting "Exact page" scope. Now only URLs with
an actual path beyond "/" trigger page scope auto-selection.

* test: update backlinks scope tests for root URL behavior change

src/client/features/backlinks/backlinksSearchScope.test.ts

@@ -16,12 +16,18 @@ describe("inferBacklinksSearchScopeFromTarget", () => {
     );
   });
 
-  it("treats explicit urls as page lookups", () => {
+  it("treats root urls with explicit protocol as domain lookups", () => {
     expect(inferBacklinksSearchScopeFromTarget("https://example.com/")).toBe(
-      "page",
+      "domain",
     );
   });
 
+  it("treats explicit urls with a path as page lookups", () => {
+    expect(
+      inferBacklinksSearchScopeFromTarget("https://example.com/pricing"),
+    ).toBe("page");
+  });
+
   it("uses inferred scope until the user overrides it", () => {
     expect(
       resolveBacklinksSearchScope({

src/client/features/backlinks/backlinksSearchScope.ts

@@ -14,7 +14,7 @@ export function inferBacklinksSearchScopeFromTarget(
     const parsed = new URL(
       hasExplicitProtocol ? trimmed : `https://${trimmed}`,
     );
-    return hasExplicitProtocol || parsed.pathname !== "/" ? "page" : "domain";
+    return parsed.pathname !== "/" ? "page" : "domain";
   } catch {
     return "domain";
   }