Remove PublicApiTests.PublicApiHasNotChanged for Datadog.Trace.dll (#6385)

## Summary of changes

Remove `PublicApiTests.PublicApiHasNotChanged` for Datadog.Trace.dll

## Reason for change

The public API surface of Datadog.Trace is not _really_ public any more,
as it's not directly referenced, so these tests are largely
unneccessary.

As of right now, `public` vs `internal` is essentially irrelevant in
this project.

## Implementation details

Remove the `PublicApiHasNotChanged` test. The other public API tests
e.g. `AssemblyReferencesHaveNotChanged` _are_ still relevant, so jumped
through some hoops to keep them

## Test coverage

Slightly less now.

## Other details

Part of stack 

- #6370
- #6376
- #6385 👈 This PR
- #6386
- #6397
- #6399
- #6400
- #6405

Author: andrewlock

tracer/test/Datadog.Trace.Tests/PublicApiTests.cs

@@ -16,13 +16,20 @@
 
 namespace Datadog.Trace.Tests.PublicApiTests
 {
-    public class DatadogTraceTests : PublicApiTestsBase
+    public class DatadogTraceTests
     {
+        private readonly PublicApiTestsBase _base;
+
         public DatadogTraceTests(ITestOutputHelper output)
-            : base(typeof(Tracer).Assembly, output)
         {
+            // We don't care about _all_ the public API tests (because this isn't _really_ public)
+            // so working around it like this
+            _base = new InternalBase(output);
         }
 
+        [Fact]
+        public void AssemblyReferencesHaveNotChanged() => _base.AssemblyReferencesHaveNotChanged();
+
 #if NETFRAMEWORK
         [Fact]
         public void ExposesTracingHttpModule()
@@ -31,6 +38,8 @@ public void ExposesTracingHttpModule()
             Assert.NotNull(httpModuleType);
         }
 #endif
+
+        private class InternalBase(ITestOutputHelper output) : PublicApiTestsBase(typeof(Tracer).Assembly, output);
     }
 
     public class DatadogTraceAnnotationsTests : PublicApiTestsBase