PERF: DataFrame.copy preserve row/column order
By passing `order="K"` we get a faster `copy`, and end up improving on a bunch of benchmarks where ArrayManager excels.  On the downside, we take a hit in some arithmetic cases which I'm still troubleshooting.  The `dropna` slowdowns in the asvs pasted below <s>should be</s>have been improved by #44857.

updated asv results

```
       before           after         ratio
     [adfc78b1]       [8605af4b]
     <fixmes23>       <perf-copy-K>
+     6.61±0.03ms      13.6±0.06ms     2.06  arithmetic.FrameWithFrameWide.time_op_different_blocks(<built-in function gt>, (1000000, 10))
+     6.84±0.08ms       12.7±0.1ms     1.85  arithmetic.FrameWithFrameWide.time_op_different_blocks(<built-in function gt>, (100000, 100))
+      15.3±0.6ms       22.6±0.2ms     1.47  arithmetic.FrameWithFrameWide.time_op_different_blocks(<built-in function add>, (1000000, 10))
+      16.8±0.2ms       23.0±0.2ms     1.37  arithmetic.FrameWithFrameWide.time_op_different_blocks(<built-in function add>, (100000, 100))
+     6.58±0.02ms      8.35±0.06ms     1.27  arithmetic.FrameWithFrameWide.time_op_different_blocks(<built-in function gt>, (10000, 1000))
+        21.5±1ms         27.3±2ms     1.27  arithmetic.FrameWithFrameWide.time_op_different_blocks(<built-in function floordiv>, (10000, 1000))
+      18.2±0.2ms       22.5±0.1ms     1.24  frame_methods.MaskBool.time_frame_mask_bools
+        24.8±2ms       30.2±0.7ms     1.22  arithmetic.FrameWithFrameWide.time_op_different_blocks(<built-in function floordiv>, (1000000, 10))
+         852±5μs      1.02±0.02ms     1.20  timeseries.AsOf.time_asof_nan_single('DataFrame')
+      22.3±0.3ms       26.5±0.8ms     1.19  arithmetic.FrameWithFrameWide.time_op_different_blocks(<built-in function floordiv>, (1000, 10000))
+        40.8±4ms       48.2±0.2ms     1.18  algos.isin.IsinWithRandomFloat.time_isin(<class 'numpy.float64'>, 750000, 'outside')
+        24.0±2ms       28.0±0.9ms     1.16  arithmetic.FrameWithFrameWide.time_op_different_blocks(<built-in function floordiv>, (100000, 100))
+      21.1±0.7ms       24.4±0.9ms     1.16  categoricals.Constructor.time_regular
+      11.4±0.2ms       13.2±0.8ms     1.15  io.pickle.Pickle.time_read_pickle
+      15.9±0.2ms         18.3±2ms     1.15  groupby.Nth.time_series_nth_all('datetime')
+        94.1±1μs         108±10μs     1.14  groupby.GroupByMethods.time_dtype_as_field('int', 'size', 'direct', 5)
+     2.65±0.03ms       2.98±0.2ms     1.12  frame_methods.Fillna.time_frame_fillna(True, 'pad', 'float32')
+      18.1±0.3ms         20.3±2ms     1.12  groupby.Nth.time_frame_nth_any('datetime')
+      8.53±0.3ms       9.48±0.3ms     1.11  arithmetic.FrameWithFrameWide.time_op_different_blocks(<built-in function gt>, (1000, 10000))
+      1.94±0.1μs      2.16±0.03μs     1.11  indexing_engines.NumericEngineIndexing.time_get_loc_near_middle((<class 'pandas._libs.index.Int8Engine'>, <class 'numpy.int8'>), 'monotonic_incr', False, 2000000)
+      1.71±0.2μs       1.90±0.2μs     1.11  index_cached_properties.IndexCache.time_inferred_type('CategoricalIndex')
+     1.68±0.02ms       1.86±0.2ms     1.11  timeseries.ResampleSeries.time_resample('datetime', '5min', 'ohlc')
+      16.1±0.1ms       17.8±0.1ms     1.10  arithmetic.FrameWithFrameWide.time_op_different_blocks(<built-in function add>, (10000, 1000))
-        138±20μs        125±0.8μs     0.91  series_methods.NanOps.time_func('sem', 1000, 'int32')
-        709±20ns         640±20ns     0.90  index_cached_properties.IndexCache.time_is_monotonic('RangeIndex')
-      24.0±0.2ms       21.6±0.3ms     0.90  frame_methods.Equals.time_frame_nonunique_unequal
-        613±60μs          551±8μs     0.90  arithmetic.IndexArithmetic.time_subtract('int')
-        215±10μs          194±4μs     0.90  algos.isin.IsIn.time_isin('Int64')
-        866±20μs         778±10μs     0.90  algos.isin.IsinAlmostFullWithRandomInt.time_isin(<class 'numpy.int64'>, 16, 'inside')
-        577±90μs         518±10μs     0.90  arithmetic.IntFrameWithScalar.time_frame_op_with_scalar(<class 'numpy.float64'>, 3.0, <built-in function le>)
-      7.83±0.2ms       7.02±0.2ms     0.90  categoricals.ValueCounts.time_value_counts(True)
-      23.9±0.2ms       21.4±0.3ms     0.89  frame_methods.Equals.time_frame_nonunique_equal
-         203±1μs          181±3μs     0.89  join_merge.Append.time_append_homogenous
-        752±10μs          669±5μs     0.89  algorithms.Quantile.time_quantile(0.5, 'higher', 'int')
-        678±30μs          600±4μs     0.89  arithmetic.IntFrameWithScalar.time_frame_op_with_scalar(<class 'numpy.float64'>, 2, <built-in function ge>)
-      2.83±0.4μs       2.50±0.1μs     0.89  index_cached_properties.IndexCache.time_shape('IntervalIndex')
-      3.75±0.2ms       3.32±0.2ms     0.88  frame_methods.Fillna.time_frame_fillna(True, 'bfill', 'float64')
-        268±30μs          237±2μs     0.88  groupby.GroupByMethods.time_dtype_as_group('object', 'unique', 'direct', 1)
-        20.2±1ms       17.9±0.1ms     0.88  groupby.Nth.time_frame_nth_any('float64')
-      24.4±0.5ms      21.5±0.09ms     0.88  frame_methods.Equals.time_frame_object_equal
-      7.43±0.4ms      6.55±0.05ms     0.88  arithmetic.FrameWithFrameWide.time_op_same_blocks(<built-in function floordiv>, (1000, 10000))
-      2.62±0.3ms      2.30±0.02ms     0.88  arithmetic.IntFrameWithScalar.time_frame_op_with_scalar(<class 'numpy.float64'>, 4, <built-in function add>)
-      8.72±0.9ms      7.65±0.09ms     0.88  algos.isin.IsinWithRandomFloat.time_isin(<class 'numpy.object_'>, 80000, 'outside')
-         600±5μs          526±6μs     0.88  arithmetic.IntFrameWithScalar.time_frame_op_with_scalar(<class 'numpy.float64'>, 3.0, <built-in function ge>)
-     1.60±0.06μs      1.40±0.05μs     0.87  indexing_engines.NumericEngineIndexing.time_get_loc((<class 'pandas._libs.index.Int64Engine'>, <class 'numpy.int64'>), 'monotonic_incr', True, 2000000)
-         160±8ms          139±8ms     0.87  algos.isin.IsInLongSeriesValuesDominate.time_isin('object', 'monotone')
-      2.62±0.3ms      2.28±0.03ms     0.87  arithmetic.IntFrameWithScalar.time_frame_op_with_scalar(<class 'numpy.float64'>, 3.0, <built-in function add>)
-     8.03±0.09ms      6.94±0.06ms     0.86  indexing.NumericSeriesIndexing.time_loc_scalar(<class 'pandas.core.indexes.numeric.UInt64Index'>, 'nonunique_monotonic_inc')
-      2.23±0.2μs       1.92±0.1μs     0.86  index_cached_properties.IndexCache.time_shape('CategoricalIndex')
-     8.04±0.07ms      6.89±0.08ms     0.86  indexing.NumericSeriesIndexing.time_getitem_scalar(<class 'pandas.core.indexes.numeric.UInt64Index'>, 'nonunique_monotonic_inc')
-        442±40μs          378±5μs     0.86  algos.isin.IsinWithArangeSorted.time_isin(<class 'numpy.float64'>, 8000)
-      1.21±0.1μs      1.04±0.08μs     0.85  index_cached_properties.IndexCache.time_values('Float64Index')
-        58.3±7μs       49.7±0.5μs     0.85  algos.isin.IsIn.time_isin_mismatched_dtype('datetime64[ns]')
-      5.20±0.1ms       4.41±0.4ms     0.85  arithmetic.NumericInferOps.time_modulo(<class 'numpy.uint64'>)
-        175±20μs          148±1μs     0.84  algos.isin.IsinAlmostFullWithRandomInt.time_isin(<class 'numpy.float64'>, 12, 'inside')
-      7.72±0.3ms      6.50±0.07ms     0.84  algorithms.Duplicated.time_duplicated(False, False, 'int')
-        819±30μs         688±20μs     0.84  algorithms.Quantile.time_quantile(0.5, 'lower', 'uint')
-      4.71±0.2μs       3.92±0.1μs     0.83  algorithms.Duplicated.time_duplicated(True, 'last', 'uint')
-      2.03±0.3μs       1.70±0.2μs     0.83  index_cached_properties.IndexCache.time_values('TimedeltaIndex')
-      1.24±0.2μs      1.03±0.03μs     0.83  index_cached_properties.IndexCache.time_values('PeriodIndex')
-      8.60±0.7ms       7.13±0.2ms     0.83  algos.isin.IsIn.time_isin('category[object]')
-      9.17±0.3ms       7.42±0.2ms     0.81  algorithms.Factorize.time_factorize(False, False, 'int')
-        186±20μs          150±3μs     0.81  algos.isin.IsIn.time_isin_empty('Int64')
-      16.7±0.3ms       13.3±0.2ms     0.80  arithmetic.Ops.time_frame_multi_and(True, 1)
-        89.7±8μs         71.0±1μs     0.79  algos.isin.IsinAlmostFullWithRandomInt.time_isin(<class 'numpy.uint64'>, 11, 'outside')
-      16.3±0.6ms       12.8±0.4ms     0.78  algorithms.Factorize.time_factorize(False, True, 'Int64')
-       700±100μs          540±4μs     0.77  arithmetic.IntFrameWithScalar.time_frame_op_with_scalar(<class 'numpy.float64'>, 3.0, <built-in function lt>)
-      10.3±0.2ms      7.84±0.09ms     0.76  arithmetic.Ops.time_frame_multi_and(True, 'default')
-     1.15±0.07ms         867±20μs     0.75  algorithms.Quantile.time_quantile(1, 'higher', 'float')
-      14.6±0.5ms       10.9±0.2ms     0.75  arithmetic.Ops.time_frame_multi_and(False, 'default')
-      14.6±0.6ms       10.9±0.2ms     0.74  arithmetic.Ops.time_frame_multi_and(False, 1)
-      34.0±0.3ms       21.6±0.2ms     0.63  frame_methods.Equals.time_frame_object_unequal
-         110±2ms       47.3±0.9ms     0.43  join_merge.ConcatDataFrames.time_c_ordered(1, False)
-         110±2ms       46.2±0.4ms     0.42  join_merge.ConcatDataFrames.time_c_ordered(1, True)
-      64.5±0.4ms       21.7±0.4ms     0.34  frame_methods.Rename.time_dict_rename_both_axes
-      64.5±0.2ms       21.7±0.3ms     0.34  frame_methods.Rename.time_rename_both_axes
-      63.3±0.3ms       20.5±0.2ms     0.32  frame_methods.Rename.time_rename_axis0
-      61.7±0.3ms       18.8±0.2ms     0.30  frame_methods.Rename.time_rename_single
-     6.02±0.06ms      1.75±0.01ms     0.29  frame_methods.Equals.time_frame_float_unequal
-      59.5±0.4ms       16.8±0.3ms     0.28  frame_methods.Rename.time_rename_axis1
```
@jbrockmendel rebase & ping when ready This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this. closing as stale