Reapply "[lldb/DWARF] Search fallback to the manual index in GetFullyQualified… (#102123)"

This reverts commit 38b67c5.

I reverted the wrong patch -- sorry :(

Author: labath

lldb/source/Plugins/SymbolFile/DWARF/DebugNamesDWARFIndex.cpp

@@ -371,6 +371,7 @@ void DebugNamesDWARFIndex::GetFullyQualifiedType(
         !ProcessEntry(entry, callback))
       return;
   }
+  m_fallback.GetFullyQualifiedType(context, callback);
 }
 
 bool DebugNamesDWARFIndex::SameParentChain(

lldb/test/Shell/SymbolFile/DWARF/x86/dwp-hash-collision.s

@@ -3,6 +3,9 @@
 ## split unit from the DWP file. This can sometimes happen when the compile unit
 ## is nearly empty (e.g. because LTO has optimized all of it away).
 
+# Is flaky on Windows on Arm.
+# UNSUPPORTED: system-windows
+
 # RUN: llvm-mc -triple=x86_64-pc-linux -filetype=obj %s --defsym MAIN=0 > %t
 # RUN: llvm-mc -triple=x86_64-pc-linux -filetype=obj %s > %t.dwp
 # RUN: %lldb %t -o "image lookup -t my_enum_type" \

lldb/test/Shell/SymbolFile/DWARF/x86/mixed-debug-names-complete-type-search.test

@@ -0,0 +1,35 @@
+REQUIRES: lld, python
+
+RUN: split-file %s %t
+RUN: %clang --target=x86_64-pc-linux -g -gpubnames -c %t/file1.c -o %t-1.o
+RUN: %clang --target=x86_64-pc-linux -g -gno-pubnames -c %t/file2.c -o %t-2.o
+RUN: llvm-dwarfdump %t-1.o --debug-names | FileCheck %s --check-prefix=PUBNAMES
+RUN: llvm-dwarfdump %t-2.o --debug-names | FileCheck %s --check-prefix=NOPUBNAMES
+RUN: ld.lld %t-1.o %t-2.o -o %t.out
+RUN: %lldb %t.out -s %t/commands -o exit | FileCheck %s
+
+// Precondition check: The first file should contain a debug_names index, but no
+// entries for MYSTRUCT.
+PUBNAMES: Name Index @ 0x0 {
+PUBNAMES-NOT: MYSTRUCT
+
+// The second file should not contain an index.
+NOPUBNAMES-NOT: Name Index
+
+// Starting from the variable in the first file, we should be able to find the
+// declaration of the type in the first unit, and then match that with the
+// definition in the second unit.
+CHECK:      (lldb) script
+CHECK:      struct MYSTRUCT {
+CHECK-NEXT:   int x;
+CHECK-NEXT: }
+
+#--- commands
+script lldb.target.FindFirstGlobalVariable("struct_ptr").GetType().GetPointeeType()
+#--- file1.c
+struct MYSTRUCT *struct_ptr;
+#--- file2.c
+struct MYSTRUCT {
+  int x;
+};
+struct MYSTRUCT struct_;