Remove deprecated code

Remove deprecated code, as part of the 3.0 release.

First merge:
- [x] #6983
- [x] #6987
- [x] #6999

The docs for this PR live [here](https://moon-ci-docs.huggingface.co/docs/datasets/pr_6996). All of your documentation changes will be reflected on that endpoint. The docs are available until 30 days after the last update.

<details>
<summary>Show benchmarks</summary>

PyArrow==8.0.0

<details>
<summary>Show updated benchmarks!</summary>

### Benchmark: benchmark_array_xd.json

| metric | read_batch_formatted_as_numpy after write_array2d | read_batch_formatted_as_numpy after write_flattened_sequence | read_batch_formatted_as_numpy after write_nested_sequence | read_batch_unformated after write_array2d | read_batch_unformated after write_flattened_sequence | read_batch_unformated after write_nested_sequence | read_col_formatted_as_numpy after write_array2d | read_col_formatted_as_numpy after write_flattened_sequence | read_col_formatted_as_numpy after write_nested_sequence | read_col_unformated after write_array2d | read_col_unformated after write_flattened_sequence | read_col_unformated after write_nested_sequence | read_formatted_as_numpy after write_array2d | read_formatted_as_numpy after write_flattened_sequence | read_formatted_as_numpy after write_nested_sequence | read_unformated after write_array2d | read_unformated after write_flattened_sequence | read_unformated after write_nested_sequence | write_array2d | write_flattened_sequence | write_nested_sequence |
|--------|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 0.005296 / 0.011353 (-0.006057) | 0.003991 / 0.011008 (-0.007017) | 0.063892 / 0.038508 (0.025384) | 0.031185 / 0.023109 (0.008076) | 0.248300 / 0.275898 (-0.027598) | 0.270326 / 0.323480 (-0.053154) | 0.004343 / 0.007986 (-0.003643) | 0.002735 / 0.004328 (-0.001594) | 0.049751 / 0.004250 (0.045501) | 0.045629 / 0.037052 (0.008577) | 0.257584 / 0.258489 (-0.000905) | 0.284697 / 0.293841 (-0.009144) | 0.029403 / 0.128546 (-0.099143) | 0.012155 / 0.075646 (-0.063491) | 0.215241 / 0.419271 (-0.204031) | 0.036258 / 0.043533 (-0.007275) | 0.246878 / 0.255139 (-0.008261) | 0.268728 / 0.283200 (-0.014472) | 0.018113 / 0.141683 (-0.123570) | 1.130733 / 1.452155 (-0.321422) | 1.205148 / 1.492716 (-0.287568) |

### Benchmark: benchmark_getitem\_100B.json

| metric | get_batch_of\_1024\_random_rows | get_batch_of\_1024\_rows | get_first_row | get_last_row |
|--------|---|---|---|---|
| new / old (diff) | 0.095196 / 0.018006 (0.077189) | 0.300741 / 0.000490 (0.300252) | 0.000220 / 0.000200 (0.000020) | 0.000043 / 0.000054 (-0.000011) |

### Benchmark: benchmark_indices_mapping.json

| metric | select | shard | shuffle | sort | train_test_split |
|--------|---|---|---|---|---|
| new / old (diff) | 0.018319 / 0.037411 (-0.019093) | 0.062766 / 0.014526 (0.048240) | 0.074748 / 0.176557 (-0.101809) | 0.122177 / 0.737135 (-0.614959) | 0.076652 / 0.296338 (-0.219687) |

### Benchmark: benchmark_iterating.json

| metric | read 5000 | read 50000 | read_batch 50000 10 | read_batch 50000 100 | read_batch 50000 1000 | read_formatted numpy 5000 | read_formatted pandas 5000 | read_formatted tensorflow 5000 | read_formatted torch 5000 | read_formatted_batch numpy 5000 10 | read_formatted_batch numpy 5000 1000 | shuffled read 5000 | shuffled read 50000 | shuffled read_batch 50000 10 | shuffled read_batch 50000 100 | shuffled read_batch 50000 1000 | shuffled read_formatted numpy 5000 | shuffled read_formatted_batch numpy 5000 10 | shuffled read_formatted_batch numpy 5000 1000 |
|--------|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 0.284508 / 0.215209 (0.069299) | 2.838298 / 2.077655 (0.760643) | 1.480098 / 1.504120 (-0.024022) | 1.362882 / 1.541195 (-0.178313) | 1.389036 / 1.468490 (-0.079454) | 0.747485 / 4.584777 (-3.837292) | 2.385333 / 3.745712 (-1.360379) | 2.924148 / 5.269862 (-2.345713) | 1.869061 / 4.565676 (-2.696616) | 0.079909 / 0.424275 (-0.344366) | 0.005173 / 0.007607 (-0.002434) | 0.345694 / 0.226044 (0.119650) | 3.430648 / 2.268929 (1.161719) | 1.837108 / 55.444624 (-53.607516) | 1.528498 / 6.876477 (-5.347979) | 1.567128 / 2.142072 (-0.574944) | 0.804615 / 4.805227 (-4.000612) | 0.135361 / 6.500664 (-6.365303) | 0.042195 / 0.075469 (-0.033274) |

### Benchmark: benchmark_map_filter.json

| metric | filter | map fast-tokenizer batched | map identity | map identity batched | map no-op batched | map no-op batched numpy | map no-op batched pandas | map no-op batched pytorch | map no-op batched tensorflow |
|--------|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 0.986240 / 1.841788 (-0.855548) | 11.428084 / 8.074308 (3.353776) | 9.168227 / 10.191392 (-1.023165) | 0.131917 / 0.680424 (-0.548507) | 0.014324 / 0.534201 (-0.519877) | 0.302188 / 0.579283 (-0.277095) | 0.263790 / 0.434364 (-0.170574) | 0.343799 / 0.540337 (-0.196539) | 0.428518 / 1.386936 (-0.958418) |

</details>
PyArrow==latest

<details>
<summary>Show updated benchmarks!</summary>

### Benchmark: benchmark_array_xd.json

| metric | read_batch_formatted_as_numpy after write_array2d | read_batch_formatted_as_numpy after write_flattened_sequence | read_batch_formatted_as_numpy after write_nested_sequence | read_batch_unformated after write_array2d | read_batch_unformated after write_flattened_sequence | read_batch_unformated after write_nested_sequence | read_col_formatted_as_numpy after write_array2d | read_col_formatted_as_numpy after write_flattened_sequence | read_col_formatted_as_numpy after write_nested_sequence | read_col_unformated after write_array2d | read_col_unformated after write_flattened_sequence | read_col_unformated after write_nested_sequence | read_formatted_as_numpy after write_array2d | read_formatted_as_numpy after write_flattened_sequence | read_formatted_as_numpy after write_nested_sequence | read_unformated after write_array2d | read_unformated after write_flattened_sequence | read_unformated after write_nested_sequence | write_array2d | write_flattened_sequence | write_nested_sequence |
|--------|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 0.005734 / 0.011353 (-0.005618) | 0.003914 / 0.011008 (-0.007094) | 0.050105 / 0.038508 (0.011596) | 0.031748 / 0.023109 (0.008639) | 0.266392 / 0.275898 (-0.009506) | 0.301221 / 0.323480 (-0.022259) | 0.004408 / 0.007986 (-0.003578) | 0.002811 / 0.004328 (-0.001517) | 0.049103 / 0.004250 (0.044853) | 0.041030 / 0.037052 (0.003978) | 0.281003 / 0.258489 (0.022513) | 0.318086 / 0.293841 (0.024245) | 0.032695 / 0.128546 (-0.095852) | 0.012239 / 0.075646 (-0.063408) | 0.060387 / 0.419271 (-0.358885) | 0.034179 / 0.043533 (-0.009354) | 0.266020 / 0.255139 (0.010881) | 0.288551 / 0.283200 (0.005351) | 0.018778 / 0.141683 (-0.122905) | 1.214959 / 1.452155 (-0.237196) | 1.268269 / 1.492716 (-0.224447) |

### Benchmark: benchmark_getitem\_100B.json

| metric | get_batch_of\_1024\_random_rows | get_batch_of\_1024\_rows | get_first_row | get_last_row |
|--------|---|---|---|---|
| new / old (diff) | 0.095449 / 0.018006 (0.077443) | 0.305733 / 0.000490 (0.305243) | 0.000216 / 0.000200 (0.000016) | 0.000052 / 0.000054 (-0.000002) |

### Benchmark: benchmark_indices_mapping.json

| metric | select | shard | shuffle | sort | train_test_split |
|--------|---|---|---|---|---|
| new / old (diff) | 0.022565 / 0.037411 (-0.014847) | 0.077266 / 0.014526 (0.062740) | 0.089345 / 0.176557 (-0.087212) | 0.128900 / 0.737135 (-0.608236) | 0.089746 / 0.296338 (-0.206593) |

### Benchmark: benchmark_iterating.json

| metric | read 5000 | read 50000 | read_batch 50000 10 | read_batch 50000 100 | read_batch 50000 1000 | read_formatted numpy 5000 | read_formatted pandas 5000 | read_formatted tensorflow 5000 | read_formatted torch 5000 | read_formatted_batch numpy 5000 10 | read_formatted_batch numpy 5000 1000 | shuffled read 5000 | shuffled read 50000 | shuffled read_batch 50000 10 | shuffled read_batch 50000 100 | shuffled read_batch 50000 1000 | shuffled read_formatted numpy 5000 | shuffled read_formatted_batch numpy 5000 10 | shuffled read_formatted_batch numpy 5000 1000 |
|--------|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 0.298221 / 0.215209 (0.083012) | 2.957671 / 2.077655 (0.880016) | 1.584674 / 1.504120 (0.080554) | 1.456906 / 1.541195 (-0.084288) | 1.467609 / 1.468490 (-0.000881) | 0.718726 / 4.584777 (-3.866051) | 0.948157 / 3.745712 (-2.797555) | 2.953559 / 5.269862 (-2.316303) | 1.895182 / 4.565676 (-2.670494) | 0.078380 / 0.424275 (-0.345895) | 0.005640 / 0.007607 (-0.001968) | 0.352978 / 0.226044 (0.126933) | 3.436341 / 2.268929 (1.167413) | 1.962418 / 55.444624 (-53.482206) | 1.655444 / 6.876477 (-5.221033) | 1.680082 / 2.142072 (-0.461990) | 0.792920 / 4.805227 (-4.012307) | 0.133518 / 6.500664 (-6.367146) | 0.041123 / 0.075469 (-0.034346) |

### Benchmark: benchmark_map_filter.json

| metric | filter | map fast-tokenizer batched | map identity | map identity batched | map no-op batched | map no-op batched numpy | map no-op batched pandas | map no-op batched pytorch | map no-op batched tensorflow |
|--------|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 1.022546 / 1.841788 (-0.819242) | 12.076711 / 8.074308 (4.002402) | 10.159920 / 10.191392 (-0.031472) | 0.143709 / 0.680424 (-0.536715) | 0.015499 / 0.534201 (-0.518702) | 0.302096 / 0.579283 (-0.277187) | 0.125202 / 0.434364 (-0.309162) | 0.349499 / 0.540337 (-0.190839) | 0.456019 / 1.386936 (-0.930917) |

</details>
</details>

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