[ This is with an updated version of the patch series submitted here ( https://sourceware.org/pipermail/gdb-patches/2023-August/201887.html ). ]

Consider the exec of test-case gdb.dwarf2/imported-unit-runto-main.exp, before adding the .gdb_index section.  It has a backward inter-cu intra-shard reference:
...
$ gdb -q -batch -iex "maint set worker-threads 0" imported-unit-runto-main
handle_deferred_entries, intra-shard case
parent map
  0x00000000000000fb 0x2935500 (deferred)
  0x00000000000000fc 0x0
parent valid map
  0x000000000000002e 0x1
  0x0000000000000045 0x0
  0x0000000000000062 0x1
  0x0000000000000084 0x0
  0x00000000000000fb 0x1
  0x0000000000000111 0x0
  0x0000000000000149 0x1
  0x00000000000002d4 0x0
handle_deferred_entries, inter-shard case
  0x00000000000000fb 0x2935500 (deferred)
  0x00000000000000fc 0x0
Resolve deferred: 0xfb -> 0xd5: no parent
...

The dependency is resolved in the inter-shard case, which assumes that all CUs have been processed, and consequently doesn't check the parent valid map.

But if we look at the parent valid map, we don't find 0xd5.  So the "no parent" is not a case of, we've processed 0xd5 and found that is has no parent, but we've not processed the PU containing 0xd5.

The problem is that we have a PU without import, and consequently no CU wins the race to read it.

This doesn't cause a problem with the current implementation (because "not processed" and "no parent" look the same), but we can reproduce the same problem with test-case forward-spec-inter-cu.exp. By changing one of the cus into a pu:
...
--- a/gdb/testsuite/gdb.dwarf2/forward-spec-inter-cu.exp
+++ b/gdb/testsuite/gdb.dwarf2/forward-spec-inter-cu.exp
@@ -48,7 +48,7 @@ Dwarf::assemble $asm_file {
     }
 
     cu {} {
-	DW_TAG_compile_unit {
+	DW_TAG_partial_unit {
 	    {DW_AT_language @DW_LANG_C_plus_plus}
 	} {
 	    declare_labels myint
...
we get:
...
FAIL: gdb.dwarf2/forward-spec-inter-cu.exp: v has a parent
...