GH-38591: [Parquet][C++] Remove redundant open calls in `ParquetFileF…

…ormat::GetReaderAsync` (#38621)

### Rationale for this change
There were duplicate method calls causing extra I/O operations, apparently unintentional from 0793432.

### What changes are included in this PR?
Remove the extra method calls.

### Are these changes tested?

### Are there any user-facing changes?

* Closes: #38591

Authored-by: Eero Lihavainen <eero.lihavainen@nitor.com>
Signed-off-by: mwish <maplewish117@gmail.com>

cpp/src/arrow/dataset/file_parquet.cc

@@ -504,11 +504,6 @@ Future<std::shared_ptr<parquet::arrow::FileReader>> ParquetFileFormat::GetReader
                                                          default_fragment_scan_options));
   auto properties = MakeReaderProperties(*this, parquet_scan_options.get(), source.path(),
                                          source.filesystem(), options->pool);
-  ARROW_ASSIGN_OR_RAISE(auto input, source.Open());
-  // TODO(ARROW-12259): workaround since we have Future<(move-only type)>
-  auto reader_fut = parquet::ParquetFileReader::OpenAsync(
-      std::move(input), std::move(properties), metadata);
-  auto path = source.path();
   auto self = checked_pointer_cast<const ParquetFileFormat>(shared_from_this());
 
   return source.OpenAsync().Then(