Centralize the home slug check on Page, case-insensitively

Elternbeirat.Contracts/Page.cs

@@ -13,6 +13,12 @@ namespace Elternbeirat.Contracts;
 /// </remarks>
 public record Page
 {
+    /// <summary>
+    ///     The slug of the home page, which is served at the site root <c>/</c> rather
+    ///     than at <c>/home</c>. Reserved: no other page may use it.
+    /// </summary>
+    private const string HomeSlug = "home";
+
     /// <summary>
     ///     Gets the PocketBase record id.
     /// </summary>
@@ -76,4 +82,18 @@ public record Page
     /// </summary>
     [JsonPropertyName("public")]
     public bool Public { get; init; }
+
+    /// <summary>
+    ///     Tests whether a slug is the home page's, ignoring case. This is the single
+    ///     definition of that comparison, so every caller treats <c>home</c> and
+    ///     <c>Home</c> alike.
+    /// </summary>
+    /// <param name="slug">
+    ///     The slug to test.
+    /// </param>
+    /// <returns>
+    ///     <see langword="true"/> if <paramref name="slug"/> is the home page's slug.
+    /// </returns>
+    public static bool IsHomeSlug(string slug) =>
+        string.Equals(slug, HomeSlug, StringComparison.OrdinalIgnoreCase);
 }