Fix contention between Clang and Carbon over external name lookup. (#7411)

The function to set the visible declarations with a given name
overwrites any existing declarations imported from an AST file, so we
need to avoid calling that for declaration contexts whose names are
managed by Clang to avoid clobbering names imported from modules.

Assisted-by: Gemini via Antigravity

toolchain/check/testdata/interop/cpp/modules/mixed_with_export.carbon

@@ -0,0 +1,53 @@
+// Part of the Carbon Language project, under the Apache License v2.0 with LLVM
+// Exceptions. See /LICENSE for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+// INCLUDE-FILE: toolchain/testing/testdata/min_prelude/full.carbon
+// EXTRA-ARGS: --clang-arg=-fmodules --clang-arg=-fmodules-cache-path=%t.cache
+//
+// AUTOUPDATE
+// TIP: To test this file alone, run:
+// TIP:   bazel test //toolchain/testing:file_test --test_arg=--file_tests=toolchain/check/testdata/interop/cpp/modules/mixed_with_export.carbon
+// TIP: To dump output, run:
+// TIP:   bazel run //toolchain/testing:file_test -- --dump_output --file_tests=toolchain/check/testdata/interop/cpp/modules/mixed_with_export.carbon
+
+// --- module.modulemap
+
+module A {
+  header "a.h"
+  export *
+}
+
+// --- a.h
+
+struct A { void F(); };
+
+struct C { void H(); };
+
+namespace N { void I(); }
+
+// --- b.carbon
+
+library "[[@TEST_NAME]]";
+
+import Cpp library "a.h";
+
+class B {
+  extend base: Cpp.A;
+  fn G(self);
+}
+
+inline Cpp '''
+Carbon::B b;
+A *a = &b;
+
+void call(C *c) {
+  a->F();
+
+  b.G();
+
+  c->H();
+
+  N::I();
+}
+''';