Enable System.Private.CoreLib for testing in CoreRun scenarios (dotnet#131493)

Enable System.Private.CoreLib for testing R2R and WASM. At least one of
the suites id known to pass with this enabled. This PR is testing to see
how many other failures there are.

---------

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Co-authored-by: Andy Ayers <andya@microsoft.com>
Copilot-Session: a5c93aa6-580b-4f11-ac30-860081fab183

Author: 3 people

src/coreclr/crossgen-corelib.proj

@@ -72,7 +72,7 @@
   </PropertyGroup>
 
   <PropertyGroup Condition="'$(PublishReadyToRunContainerFormat)' == 'wasm'">
-    <CrossgenCoreLibOutputPath>$([MSBuild]::NormalizePath('$(BinDir)', '$(CoreLibAssemblyName).NotReadyYet.wasm'))</CrossgenCoreLibOutputPath>
+    <CrossgenCoreLibOutputPath>$([MSBuild]::NormalizePath('$(BinDir)', '$(CoreLibAssemblyName).wasm'))</CrossgenCoreLibOutputPath>
   </PropertyGroup>
 
   <PropertyGroup Condition="'$(UseComposite)' == 'true'">

src/coreclr/hosts/corerun/corerun.cpp

@@ -385,6 +385,10 @@ static bool HOST_CONTRACT_CALLTYPE external_assembly_probe(
         std::string full_path = dir;
         assert(full_path.back() == pal::dir_delim);
         full_path.append(name);
+#ifdef TARGET_BROWSER
+        if (BrowserHost_ExternalAssemblyProbe(full_path.c_str(), data_start, size))
+            return true;
+#endif // TARGET_BROWSER
         if (pal::try_map_file_readonly(full_path.c_str(), data_start, size))
             return true;
     }