It's not exactly clear what the absolute minimal reproducer is here, but it seems that for certain combinations of arrays, sub-objects, and computed projections, the classic engine can produce output with fields reordered relative to their position in the inclusion projection.

For example, given an input document

{
  _id: 1,
  'array': [],
  'obj': {},
}

and pipeline

[{$project: {
  'array': [],
  'obj.array': []
}}]

we produce

{
  '_id': 1,
  'obj': {'array': []},
  'array': []
}

This problem seems to go back quite a long way (at least 4.2), but was recently surfaced by the aggregation_optimization_fuzzer in BF-24359 (it appears we do not have the same behavior in SBE).