Creating a list with Thread

The easiest way to achieve this is with MapIndexed:

MapIndexed[
  {#2[[1]], #1} &,
  aaah,
  {2}
]

{{{1, 11}, {1, 21}, {1, 31}}, {{2, 12}, {2, 22}, {2, 32}}, {{3, 13}, {3, 23}, {3, 33}}}

MapIndexed[Thread @ {First @ #2, #} &] @ aaah

{{{1, 11}, {1, 21}, {1, 31}},
{{2, 12}, {2, 22}, {2, 32}}, 
{{3, 13}, {3, 23}, {3, 33}}}

I think that the most natural way of doing this is by using MapIndexed. But if you want to use Range and Thread, this is one way:

{{11, 21, 31}, {12, 22, 32}, {13, 23, 33}} //
  {Length /* Range, Identity} //
  Through //
  Thread //
  Map[Thread]

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