BUG: cast to correct dtype in Index.drop()
State: closed

- [x] closes #18304
- [x] tests added / passed
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [x] whatsnew entry


Labels:
name: Bug
name: Reshaping
description: Concat, Merge/Join, Stack/Unstack, Explode
name: Dtype Conversions
description: Unexpected or buggy dtype conversions

Comments:
# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=h1) Report
> Merging [#18309](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/9c799e2c4331e5e42cfda03323eef165feb5be1a?src=pr&el=desc) will **decrease** coverage by `0.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/18309/graphs/tree.svg?src=pr&token=eZ4WkYLtcO&width=650&height=150)](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #18309      +/-   ##
==========================================
- Coverage   91.39%   91.38%   -0.02%     
==========================================
  Files         164      164              
  Lines       49854    49855       +1     
==========================================
- Hits        45566    45558       -8     
- Misses       4288     4297       +9
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `89.18% <100%> (ø)` | :arrow_up: |
| #single | `39.44% <100%> (-0.06%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/indexes/base.py](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9iYXNlLnB5) | `96.42% <100%> (ø)` | :arrow_up: |
| [pandas/core/common.py](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29tbW9uLnB5) | `93% <100%> (ø)` | :arrow_up: |
| [pandas/io/gbq.py](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=tree#diff-cGFuZGFzL2lvL2dicS5weQ==) | `25% <0%> (-58.34%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.8% <0%> (-0.1%)` | :arrow_down: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=footer). Last update [9c799e2...7614bf3](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).

# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=h1) Report
> Merging [#18309](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/dbec3c92e08063d247e0d28937c8695bbd66fe94?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/18309/graphs/tree.svg?src=pr&token=eZ4WkYLtcO&height=150&width=650)](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #18309      +/-   ##
==========================================
+ Coverage    91.6%   91.61%   +<.01%     
==========================================
  Files         150      150              
  Lines       48939    48940       +1     
==========================================
+ Hits        44833    44834       +1     
  Misses       4106     4106
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `89.97% <100%> (ø)` | :arrow_up: |
| #single | `41.17% <100%> (ø)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/common.py](https://codecov.io/gh/pandas-dev/pandas/pull/18309/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29tbW9uLnB5) | `92.92% <100%> (ø)` | :arrow_up: |
| [pandas/core/indexes/base.py](https://codecov.io/gh/pandas-dev/pandas/pull/18309/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9iYXNlLnB5) | `96.45% <100%> (ø)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=footer). Last update [dbec3c9...7fea97a](https://codecov.io/gh/pandas-dev/pandas/pull/18309?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).

can you rebase
thanks @toobaz