Add regression tests for path casing normalization

PathUtilL0:
- Folder casing normalization (create MiXeDcAsE, query lowercase)
- Idempotency (calling twice returns same result)
- Input casing independence (upper and lower resolve to same canonical)

HostContextL0:
- Root directory returns cached value across calls
- Derived paths (Diag, Externals) share Root prefix casing

Author: salmanmkc

src/Test/L0/HostContextL0.cs

@@ -299,6 +299,52 @@ public async Task AuthMigrationAutoReset()
             }
         }
 
+        [Fact]
+        [Trait("Level", "L0")]
+        [Trait("Category", "Common")]
+        public void GetDirectoryRootReturnsCachedValue()
+        {
+            try
+            {
+                Setup();
+
+                // Call GetDirectory(Root) twice — should return the same reference
+                var root1 = _hc.GetDirectory(WellKnownDirectory.Root);
+                var root2 = _hc.GetDirectory(WellKnownDirectory.Root);
+
+                Assert.NotNull(root1);
+                Assert.Equal(root1, root2);
+                Assert.True(Directory.Exists(root1));
+            }
+            finally
+            {
+                Teardown();
+            }
+        }
+
+        [Fact]
+        [Trait("Level", "L0")]
+        [Trait("Category", "Common")]
+        public void GetDirectoryDerivedPathsUseRootCasing()
+        {
+            try
+            {
+                Setup();
+
+                var root = _hc.GetDirectory(WellKnownDirectory.Root);
+                var diag = _hc.GetDirectory(WellKnownDirectory.Diag);
+                var externals = _hc.GetDirectory(WellKnownDirectory.Externals);
+
+                // Diag and Externals should start with the same Root prefix
+                Assert.StartsWith(root, diag);
+                Assert.StartsWith(root, externals);
+            }
+            finally
+            {
+                Teardown();
+            }
+        }
+
         private void Setup([CallerMemberName] string testName = "")
         {
             _tokenSource = new CancellationTokenSource();

src/Test/L0/Util/PathUtilL0.cs

@@ -78,6 +78,74 @@ public void GetCanonicalPath_NormalizesDriveLetter_OnWindows()
             Assert.True(char.IsUpper(result[0]),
                 $"Expected uppercase drive letter but got: {result}");
         }
+
+        [Fact]
+        [Trait("Level", "L0")]
+        [Trait("Category", "Common")]
+        public void GetCanonicalPath_NormalizesFolderCasing_OnWindows()
+        {
+            // Create a directory with known casing, then query with wrong casing
+            var basePath = Path.GetTempPath();
+            if (basePath.StartsWith(@"\\"))
+            {
+                return; // Skip UNC
+            }
+
+            var realName = "PathUtilTest_MiXeDcAsE_" + Path.GetRandomFileName();
+            var realDir = Path.Combine(basePath, realName);
+            try
+            {
+                Directory.CreateDirectory(realDir);
+
+                // Query with all-lowercase version
+                var wrongCased = Path.Combine(basePath, realName.ToLowerInvariant());
+
+                var result = PathUtil.GetCanonicalPath(wrongCased);
+
+                // The canonical result should contain the original mixed-case name
+                Assert.Contains(realName, result);
+            }
+            finally
+            {
+                if (Directory.Exists(realDir))
+                {
+                    Directory.Delete(realDir);
+                }
+            }
+        }
+
+        [Fact]
+        [Trait("Level", "L0")]
+        [Trait("Category", "Common")]
+        public void GetCanonicalPath_IsIdempotent_OnWindows()
+        {
+            // Calling GetCanonicalPath twice should return the same result
+            var tempDir = Path.GetTempPath().TrimEnd(Path.DirectorySeparatorChar);
+            var first = PathUtil.GetCanonicalPath(tempDir);
+            var second = PathUtil.GetCanonicalPath(first);
+            Assert.Equal(first, second);
+        }
+
+        [Fact]
+        [Trait("Level", "L0")]
+        [Trait("Category", "Common")]
+        public void GetCanonicalPath_ReturnsSameResult_RegardlessOfInputCasing_OnWindows()
+        {
+            var tempDir = Path.GetTempPath().TrimEnd(Path.DirectorySeparatorChar);
+            if (tempDir.StartsWith(@"\\"))
+            {
+                return; // Skip UNC
+            }
+
+            var upper = tempDir.ToUpperInvariant();
+            var lower = tempDir.ToLowerInvariant();
+
+            var resultUpper = PathUtil.GetCanonicalPath(upper);
+            var resultLower = PathUtil.GetCanonicalPath(lower);
+
+            // Both should resolve to the same canonical path
+            Assert.Equal(resultUpper, resultLower);
+        }
 #endif
     }
 }