Is your feature request related to a problem or challenge? Please describe what you are trying to do.
When writing parquet files, depending on the writer settings and the data being written, we have observed the ArrowWriter consuming large amounts of memory (10s of GB) -- see #5828

The memory usage of parquet writers also often comes up in the context of proposals for new parquet formats

There is already a discussion about how to limit memory when writing here https://docs.rs/parquet/latest/parquet/arrow/arrow_writer/struct.ArrowWriter.html#memory-limiting

However there is now way currently to get a measurement of actual current use (that we could use to abort the write, for example).

Describe the solution you'd like

I would like some way to get to have some visibility on the current memory usage of the internal buffering in the parquet writer

Describe alternatives you've considered
I propose adding a function to ArrowWriter modeled on Array::get_array_memory_size

impl ArrayWriter {
  /// returns an estimate of how much memory the array
  /// writer is currently using in its internal buffers. 
  fn memory_size(&self) -> usize { ... }
...
}

Additional context
Here is one ticket that describes one non trivial source of memory usage #5828 so the indices should be included.