Title: Better error handling in `dataset_module_factory`
State: closed

cc @cakiki who reported it on [slack](https://huggingface.slack.com/archives/C039P47V1L5/p1717754405578539) (private link)

This PR updates how errors are handled in `dataset_module_factory` when the  `dataset_info` cannot be accessed:
1. Use multiple `except ... as e` instead of using `isinstance(e, ...)`
2. Always raise `DatasetNotFoundError` with `from e` so that the initial error is explicitly logged in the stacktrace.
3. Differentiate `RepoNotFoundError` / `GatedRepoError` / `RevisionNotFoundError` cases

Comments:
The docs for this PR live [here](https://moon-ci-docs.huggingface.co/docs/datasets/pr_6959). All of your documentation changes will be reflected on that endpoint. The docs are available until 30 days after the last update.

Test should be fixed by https://github.com/huggingface/datasets/pull/6959/commits/ef8f7cee79ffb070d9b5190f21128fc523b3d3ee (tested locally). Let's see what CI says :crossed_fingers: 

<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) | 0.005678 / 0.011353 (-0.005675) | 0.004119 / 0.011008 (-0.006889) | 0.063901 / 0.038508 (0.025393) | 0.032071 / 0.023109 (0.008961) | 0.243182 / 0.275898 (-0.032716) | 0.280709 / 0.323480 (-0.042770) | 0.004195 / 0.007986 (-0.003791) | 0.002810 / 0.004328 (-0.001518) | 0.048722 / 0.004250 (0.044472) | 0.049381 / 0.037052 (0.012328) | 0.257816 / 0.258489 (-0.000673) | 0.288460 / 0.293841 (-0.005381) | 0.028518 / 0.128546 (-0.100029) | 0.010775 / 0.075646 (-0.064871) | 0.203149 / 0.419271 (-0.216122) | 0.038792 / 0.043533 (-0.004741) | 0.248502 / 0.255139 (-0.006637) | 0.268251 / 0.283200 (-0.014949) | 0.019536 / 0.141683 (-0.122147) | 1.133935 / 1.452155 (-0.318220) | 1.182855 / 1.492716 (-0.309862) |

### 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) | 0.097531 / 0.018006 (0.079525) | 0.303612 / 0.000490 (0.303122) | 0.000222 / 0.000200 (0.000022) | 0.000044 / 0.000054 (-0.000011) |

### Benchmark: benchmark_indices_mapping.json

| metric | select | shard | shuffle | sort | train_test_split |
|--------|---|---|---|---|---|
| new / old (diff) | 0.019670 / 0.037411 (-0.017741) | 0.063439 / 0.014526 (0.048913) | 0.075119 / 0.176557 (-0.101438) | 0.122419 / 0.737135 (-0.614717) | 0.076965 / 0.296338 (-0.219374) |

### 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) | 0.286780 / 0.215209 (0.071571) | 2.811860 / 2.077655 (0.734206) | 1.485165 / 1.504120 (-0.018954) | 1.373296 / 1.541195 (-0.167898) | 1.412700 / 1.468490 (-0.055790) | 0.566442 / 4.584777 (-4.018335) | 2.382616 / 3.745712 (-1.363096) | 2.677214 / 5.269862 (-2.592647) | 1.760073 / 4.565676 (-2.805603) | 0.062673 / 0.424275 (-0.361602) | 0.005050 / 0.007607 (-0.002557) | 0.341701 / 0.226044 (0.115657) | 3.321182 / 2.268929 (1.052253) | 1.811715 / 55.444624 (-53.632909) | 1.554986 / 6.876477 (-5.321491) | 1.727448 / 2.142072 (-0.414624) | 0.642193 / 4.805227 (-4.163034) | 0.117878 / 6.500664 (-6.382786) | 0.042814 / 0.075469 (-0.032655) |

### 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) | 0.985894 / 1.841788 (-0.855894) | 12.195975 / 8.074308 (4.121667) | 9.890180 / 10.191392 (-0.301212) | 0.142638 / 0.680424 (-0.537786) | 0.015207 / 0.534201 (-0.518994) | 0.283140 / 0.579283 (-0.296143) | 0.266016 / 0.434364 (-0.168348) | 0.325518 / 0.540337 (-0.214820) | 0.418994 / 1.386936 (-0.967942) |

</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) | 0.005978 / 0.011353 (-0.005374) | 0.003915 / 0.011008 (-0.007093) | 0.051592 / 0.038508 (0.013084) | 0.033338 / 0.023109 (0.010229) | 0.267925 / 0.275898 (-0.007973) | 0.296011 / 0.323480 (-0.027469) | 0.004503 / 0.007986 (-0.003483) | 0.002854 / 0.004328 (-0.001475) | 0.049958 / 0.004250 (0.045707) | 0.041708 / 0.037052 (0.004656) | 0.287185 / 0.258489 (0.028696) | 0.322715 / 0.293841 (0.028874) | 0.030088 / 0.128546 (-0.098458) | 0.010709 / 0.075646 (-0.064938) | 0.059736 / 0.419271 (-0.359536) | 0.034294 / 0.043533 (-0.009239) | 0.264316 / 0.255139 (0.009177) | 0.285471 / 0.283200 (0.002272) | 0.019197 / 0.141683 (-0.122486) | 1.135571 / 1.452155 (-0.316583) | 1.190019 / 1.492716 (-0.302698) |

### 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) | 0.099251 / 0.018006 (0.081245) | 0.305357 / 0.000490 (0.304867) | 0.000215 / 0.000200 (0.000015) | 0.000045 / 0.000054 (-0.000010) |

### Benchmark: benchmark_indices_mapping.json

| metric | select | shard | shuffle | sort | train_test_split |
|--------|---|---|---|---|---|
| new / old (diff) | 0.023206 / 0.037411 (-0.014205) | 0.077835 / 0.014526 (0.063310) | 0.090242 / 0.176557 (-0.086315) | 0.131208 / 0.737135 (-0.605928) | 0.091726 / 0.296338 (-0.204612) |

### 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) | 0.292487 / 0.215209 (0.077278) | 2.837044 / 2.077655 (0.759389) | 1.553155 / 1.504120 (0.049035) | 1.433645 / 1.541195 (-0.107550) | 1.476702 / 1.468490 (0.008212) | 0.561926 / 4.584777 (-4.022851) | 0.954630 / 3.745712 (-2.791082) | 2.752286 / 5.269862 (-2.517575) | 1.782746 / 4.565676 (-2.782931) | 0.062984 / 0.424275 (-0.361291) | 0.005056 / 0.007607 (-0.002551) | 0.341700 / 0.226044 (0.115656) | 3.343726 / 2.268929 (1.074798) | 1.953390 / 55.444624 (-53.491234) | 1.616989 / 6.876477 (-5.259488) | 1.785104 / 2.142072 (-0.356969) | 0.643465 / 4.805227 (-4.161763) | 0.115905 / 6.500664 (-6.384759) | 0.041678 / 0.075469 (-0.033791) |

### 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) | 1.000237 / 1.841788 (-0.841550) | 12.633517 / 8.074308 (4.559208) | 10.553485 / 10.191392 (0.362092) | 0.143188 / 0.680424 (-0.537236) | 0.016020 / 0.534201 (-0.518181) | 0.286739 / 0.579283 (-0.292544) | 0.128488 / 0.434364 (-0.305876) | 0.321932 / 0.540337 (-0.218405) | 0.418635 / 1.386936 (-0.968301) |

</details>
</details>

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