Fix flow analysis of extern local functions

src/Compilers/CSharp/Portable/FlowAnalysis/AbstractFlowPass.cs

@@ -1403,7 +1403,8 @@ protected virtual void VisitLocalFunctionUse(
             SyntaxNode syntax,
             bool isCall)
         {
-            if (isCall)
+            // Extern local function bodies are not visited, so ignore their state.
+            if (isCall && !symbol.IsExtern)
             {
                 Join(ref State, ref localFunctionState.StateFromBottom);
 

src/Compilers/CSharp/Test/Emit3/FlowAnalysis/FlowTests.cs

@@ -6103,5 +6103,66 @@ public Base(int x){}
                 Diagnostic(ErrorCode.ERR_ParamUnassigned, "C").WithArguments("a").WithLocation(1, 7)
                 );
         }
+
+        [Fact]
+        public void OutParameterIsNotAssigned_LocalFunction()
+        {
+            var source = """
+                class C
+                {
+                    void M(out int i)
+                    {
+                        f();
+                        static void f() { }
+                    }
+                }
+                """;
+            CreateCompilation(source).VerifyDiagnostics(
+                // (3,10): error CS0177: The out parameter 'i' must be assigned to before control leaves the current method
+                //     void M(out int i)
+                Diagnostic(ErrorCode.ERR_ParamUnassigned, "M").WithArguments("i").WithLocation(3, 10));
+        }
+
+        [Fact, WorkItem("https://github.com/dotnet/roslyn/issues/79437")]
+        public void OutParameterIsNotAssigned_LocalFunction_Extern()
+        {
+            var source = """
+                using System.Runtime.InteropServices;
+                class C
+                {
+                    void M(out int i)
+                    {
+                        f();
+                        [DllImport("test")] static extern void f();
+                    }
+                }
+                """;
+            CreateCompilation(source).VerifyDiagnostics(
+                // (4,10): error CS0177: The out parameter 'i' must be assigned to before control leaves the current method
+                //     void M(out int i)
+                Diagnostic(ErrorCode.ERR_ParamUnassigned, "M").WithArguments("i").WithLocation(4, 10));
+        }
+
+        [Fact, WorkItem("https://github.com/dotnet/roslyn/issues/79437")]
+        public void UnassignedVariable_LocalFunction_Extern()
+        {
+            var source = """
+                using System.Runtime.InteropServices;
+                class C
+                {
+                    void M()
+                    {
+                        int i;
+                        f();
+                        i.ToString();
+                        [DllImport("test")] extern static void f();
+                    }
+                }
+                """;
+            CreateCompilation(source).VerifyDiagnostics(
+                // (8,9): error CS0165: Use of unassigned local variable 'i'
+                //         i.ToString();
+                Diagnostic(ErrorCode.ERR_UseDefViolation, "i").WithArguments("i").WithLocation(8, 9));
+        }
     }
 }

src/Compilers/CSharp/Test/Emit3/FlowAnalysis/LocalFunctions.cs

@@ -705,6 +705,25 @@ public static void Main()
                 Diagnostic(ErrorCode.WRN_UnreferencedLocalFunction, "Local").WithArguments("Local").WithLocation(7, 14));
         }
 
+        [Fact]
+        public void UnusedLocalFunc_Extern()
+        {
+            var comp = CreateCompilation("""
+                using System.Runtime.InteropServices;
+                class C
+                {
+                    public static void Main()
+                    {
+                        [DllImport("test")] static extern bool Local();
+                    }
+                }
+                """);
+            comp.VerifyDiagnostics(
+                // (6,48): warning CS8321: The local function 'Local' is declared but never used
+                //         [DllImport("test")] static extern bool Local();
+                Diagnostic(ErrorCode.WRN_UnreferencedLocalFunction, "Local").WithArguments("Local").WithLocation(6, 48));
+        }
+
         [Fact]
         public void UnassignedInStruct()
         {