[OpenMP] Fix test after updating library search paths (#83573)

Summary:
We still use this bitcode library in one case, the NVPTX non-LTO build.
The patch updated the search paths to treat it the same as other
libraries, which unintentionally prioritized system paths over
LIBRARY_PATH which is generally not correct. Also we had a test that
relied on system state so remove that.

Author: jhuber6

clang/lib/Driver/ToolChains/CommonArgs.cpp

@@ -2767,10 +2767,6 @@ void tools::addOpenMPDeviceRTL(const Driver &D,
                                const ToolChain &HostTC) {
   SmallVector<StringRef, 8> LibraryPaths;
 
-  // Check all of the standard library search paths used by the compiler.
-  for (const auto &LibPath : HostTC.getFilePaths())
-    LibraryPaths.emplace_back(LibPath);
-
   // Add user defined library paths from LIBRARY_PATH.
   std::optional<std::string> LibPath =
       llvm::sys::Process::GetEnv("LIBRARY_PATH");
@@ -2782,6 +2778,10 @@ void tools::addOpenMPDeviceRTL(const Driver &D,
       LibraryPaths.emplace_back(Path.trim());
   }
 
+  // Check all of the standard library search paths used by the compiler.
+  for (const auto &LibPath : HostTC.getFilePaths())
+    LibraryPaths.emplace_back(LibPath);
+
   OptSpecifier LibomptargetBCPathOpt =
       Triple.isAMDGCN() ? options::OPT_libomptarget_amdgpu_bc_path_EQ
                         : options::OPT_libomptarget_nvptx_bc_path_EQ;

clang/test/Driver/openmp-offload-gpu.c

@@ -101,17 +101,6 @@
 
 /// ###########################################################################
 
-/// Check that the warning is thrown when the libomptarget bitcode library is not found.
-/// Libomptarget requires sm_52 or newer so an sm_52 bitcode library should never exist.
-// RUN:   not %clang -### -fopenmp=libomp -fopenmp-targets=nvptx64-nvidia-cuda \
-// RUN:   -Xopenmp-target -march=sm_52 --cuda-path=%S/Inputs/CUDA_102/usr/local/cuda \
-// RUN:   -fopenmp-relocatable-target -save-temps %s 2>&1 \
-// RUN:   | FileCheck -check-prefix=CHK-BCLIB-WARN %s
-
-// CHK-BCLIB-WARN: no library 'libomptarget-nvptx-sm_52.bc' found in the default clang lib directory or in LIBRARY_PATH; use '--libomptarget-nvptx-bc-path' to specify nvptx bitcode library
-
-/// ###########################################################################
-
 /// Check that the error is thrown when the libomptarget bitcode library does not exist.
 // RUN:   not %clang -### -fopenmp=libomp -fopenmp-targets=nvptx64-nvidia-cuda \
 // RUN:   -Xopenmp-target -march=sm_52 --cuda-path=%S/Inputs/CUDA_102/usr/local/cuda \