[C++][Parquet] parquet-writer-test Large memory tests fail on TestColumnWriter.WriteLargeDictEncodedPage and TestColumnWriter.ThrowsOnDictIndicesTooLarge

### Describe the bug, including details regarding any error messages, version, and platform.

We are trying to enable a new CI job for Large Memory tests.

The job is successful except for `parquet-writer-test`:
```
[ RUN ] TestColumnWriter.WriteLargeDictEncodedPage
/arrow/cpp/src/parquet/column_writer_test.cc:1100: Failure
Expected equality of these values:
page_count
Which is: 7501
2
[ FAILED ] TestColumnWriter.WriteLargeDictEncodedPage (4223 ms)
[ RUN ] TestColumnWriter.ThrowsOnDictIndicesTooLarge
/arrow/cpp/src/parquet/column_writer_test.cc:1147: Failure
Expected: try { ([&]() { file_writer->Close(); })(); } catch (const ParquetException& err) { switch (0) case 0: default: if (const ::testing::AssertionResult gtest_ar = (::testing::internal::MakePredicateFormatterFromMatcher((::testing::Property(&ParquetException::what, ::testing::HasSubstr("exceeds maximum int value"))))("err", err))) ; else ::testing::internal::AssertHelper(::testing::TestPartResult::kNonFatalFailure, "/arrow/cpp/src/parquet/column_writer_test.cc", 1147, gtest_ar.failure_message()) = ::testing::Message(); throw; } throws an exception of type ParquetException.
Actual: it throws nothing.
[ FAILED ] TestColumnWriter.ThrowsOnDictIndicesTooLarge (28941 ms)
```

I can reproduce the failures locally when building with `ARROW_LARGE_MEMORY_TESTS=ON` .

### Component(s)

C++, Parquet