Fix static extension method not showing up on enum type

src/EditorFeatures/Test2/IntelliSense/CSharpCompletionCommandHandlerTests.vb

@@ -12998,6 +12998,32 @@ public class Class1
             End Using
         End Function
 
+        <WpfTheory, CombinatorialData>
+        <WorkItem("https://github.com/dotnet/roslyn/issues/79444")>
+        Public Async Function TestStaticExtensionMethod_OnEnumType(showCompletionInArgumentLists As Boolean) As Task
+            Using state = TestStateFactory.CreateCSharpTestState(
+                <Document>
+                using System;
+
+                E.$$
+
+                enum E;
+
+                static class C
+                {
+                    extension(E)
+                    {
+                        public static void EM() { }
+                    }
+                }
+                </Document>,
+                showCompletionInArgumentLists:=showCompletionInArgumentLists, languageVersion:=LanguageVersionExtensions.CSharpNext)
+
+                state.SendInvokeCompletionList()
+                Await state.AssertCompletionItemsContain("EM", displayTextSuffix:="")
+            End Using
+        End Function
+
         <WorkItem("https://github.com/dotnet/roslyn/issues/78284")>
         <WpfTheory, CombinatorialData>
         Public Async Function TestOverrideInstanceAssignmentOperator(showCompletionInArgumentLists As Boolean) As Task

src/Features/CSharp/Portable/Completion/CompletionProviders/EnumAndCompletionListTagCompletionProvider.cs

@@ -23,10 +23,12 @@
 
 namespace Microsoft.CodeAnalysis.CSharp.Completion.Providers;
 
-[ExportCompletionProvider(nameof(EnumAndCompletionListTagCompletionProvider), LanguageNames.CSharp)]
+[ExportCompletionProvider(nameof(EnumAndCompletionListTagCompletionProvider), LanguageNames.CSharp), Shared]
 [ExtensionOrder(After = nameof(CSharpSuggestionModeCompletionProvider))]
-[Shared]
-internal sealed partial class EnumAndCompletionListTagCompletionProvider : LSPCompletionProvider
+[method: ImportingConstructor]
+[method: Obsolete(MefConstruction.ImportingConstructorMessage, error: true)]
+internal sealed partial class EnumAndCompletionListTagCompletionProvider()
+    : LSPCompletionProvider
 {
     private static readonly CompletionItemRules s_enumTypeRules =
         CompletionItemRules.Default.WithCommitCharacterRules([CharacterSetModificationRule.Create(CharacterSetModificationKind.Replace, '.')])
@@ -35,12 +37,6 @@ internal sealed partial class EnumAndCompletionListTagCompletionProvider : LSPCo
 
     private static readonly ImmutableHashSet<char> s_triggerCharacters = [' ', '[', '(', '~'];
 
-    [ImportingConstructor]
-    [Obsolete(MefConstruction.ImportingConstructorMessage, error: true)]
-    public EnumAndCompletionListTagCompletionProvider()
-    {
-    }
-
     internal override string Language => LanguageNames.CSharp;
 
     public override bool IsInsertionTrigger(SourceText text, int characterPosition, CompletionOptions options)
@@ -105,7 +101,12 @@ public override async Task ProvideCompletionsAsync(CompletionContext context)
     }
 
     private static async Task HandleSingleTypeAsync(
-        CompletionContext context, SemanticModel semanticModel, SyntaxToken token, ITypeSymbol type, bool isParams, CancellationToken cancellationToken)
+        CompletionContext context,
+        SemanticModel semanticModel,
+        SyntaxToken token,
+        ITypeSymbol type,
+        bool isParams,
+        CancellationToken cancellationToken)
     {
         if (isParams && type is IArrayTypeSymbol arrayType)
             type = arrayType.ElementType;

src/Features/Core/Portable/Completion/Providers/AbstractSymbolCompletionProvider.cs

@@ -13,7 +13,6 @@
 using Microsoft.CodeAnalysis.Internal.Log;
 using Microsoft.CodeAnalysis.LanguageService;
 using Microsoft.CodeAnalysis.PooledObjects;
-using Microsoft.CodeAnalysis.Shared.Collections;
 using Microsoft.CodeAnalysis.Shared.Extensions;
 using Microsoft.CodeAnalysis.Shared.Extensions.ContextQuery;
 using Microsoft.CodeAnalysis.Shared.Utilities;

src/Workspaces/Core/Portable/Recommendations/AbstractRecommendationService.cs

@@ -113,7 +113,9 @@ internal bool ShouldIncludeSymbol(ISymbol symbol)
 
             if (_context.IsEnumTypeMemberAccessContext)
             {
-                return symbol.Kind == SymbolKind.Field;
+                // Within an enum type, we can access fields of the enum, as well as static extensions on that type.
+                return symbol.Kind == SymbolKind.Field ||
+                     symbol is { IsStatic: true, ContainingType.IsExtension: true };
             }
 
             // In an expression or statement context, we don't want to display instance members declared in outer containing types.