Add test for no logo and active nav

Author: cderv

tests/docs/smoke-all/website-sidebar/issue-13506-no-logo/.gitignore

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+/.quarto/
+**/*.quarto_ipynb

tests/docs/smoke-all/website-sidebar/issue-13506-no-logo/_quarto.yml

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+project:
+  type: website
+
+website:
+  title: "Issue 13506 - No Logo"
+  navbar:
+    left:
+      - text: "Section A"
+        href: index.qmd
+      - text: "Section B"
+        href: page2.qmd
+  sidebar:
+    - title: "Section A"
+      contents:
+        - index.qmd
+    - title: "Section B"
+      contents:
+        - page2.qmd
+
+format:
+  html:
+    theme: cosmo

tests/docs/smoke-all/website-sidebar/issue-13506-no-logo/index.qmd

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+---
+title: "Section A"
+_quarto:
+  tests:
+    html:
+      ensureHtmlElements:
+        -
+          - 'nav.navbar a.nav-link[href$="index.html"].active'
+          - 'nav.navbar a.nav-link[href$="page2.html"]:not(.active)'
+        -
+          - 'a.sidebar-logo-link'
+---
+
+## Section A
+
+This is Section A. When NO logo is configured in the sidebar, the navbar active
+state should work correctly. The "Section A" navbar item should be active on this page.
+
+The bug (issue #13506): After PR #12996, `sidebar.logo` was normalized to
+`{light: undefined, dark: undefined}`, making `if(sidebar.logo)` always true.
+This created empty `<a class="sidebar-logo-link">` elements that interfered with
+the navbar active state detection logic.
+
+See also: [Section B](page2.qmd)

tests/docs/smoke-all/website-sidebar/issue-13506-no-logo/page2.qmd

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+---
+title: "Section B"
+_quarto:
+  tests:
+    html:
+      ensureHtmlElements:
+        -
+          - 'nav.navbar a.nav-link[href$="page2.html"].active'
+          - 'nav.navbar a.nav-link[href$="index.html"]:not(.active)'
+        -
+          - 'a.sidebar-logo-link'
+---
+
+## Section B
+
+This is Section B. The "Section B" navbar item should be active on this page,
+demonstrating that the navbar active state detection works correctly without
+empty logo links interfering.
+
+See also: [Section A](index.qmd)