BUG-24212 fix when other_index has incompatible dtype
- [X] closes #25001
- [X] tests added / passed
- [X] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [ ] whatsnew entry

Followup to #24916, addresses the case when the other index has an incompatible dtype, so we cannot take directly from it. Currently, this PR ~naively replaces the missing index values with the number of the rows in the other index that caused them~ replaces the missing index values with the appropriate NA value.

~Still working on adding cases when it is possible to combine indices of sparse/categorical dtypes without densifying.~
# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/25009?src=pr&el=h1) Report
> Merging [#25009](https://codecov.io/gh/pandas-dev/pandas/pull/25009?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/abf0824200a34c00f6a20b283bbb968f2c2d288f?src=pr&el=desc) will **decrease** coverage by `49.49%`.
> The diff coverage is `0%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/25009/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/25009?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #25009      +/-   ##
==========================================
- Coverage   92.38%   42.88%   -49.5%     
==========================================
  Files         166      166              
  Lines       52401    52407       +6     
==========================================
- Hits        48409    22475   -25934     
- Misses       3992    29932   +25940
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `?` | |
| #single | `42.88% <0%> (-0.01%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/25009?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/reshape/merge.py](https://codecov.io/gh/pandas-dev/pandas/pull/25009/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvcmVzaGFwZS9tZXJnZS5weQ==) | `9.43% <0%> (-85.05%)` | :arrow_down: |
| [pandas/io/formats/latex.py](https://codecov.io/gh/pandas-dev/pandas/pull/25009/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2Zvcm1hdHMvbGF0ZXgucHk=) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/core/categorical.py](https://codecov.io/gh/pandas-dev/pandas/pull/25009/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY2F0ZWdvcmljYWwucHk=) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/io/sas/sas\_constants.py](https://codecov.io/gh/pandas-dev/pandas/pull/25009/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL3Nhcy9zYXNfY29uc3RhbnRzLnB5) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/tseries/plotting.py](https://codecov.io/gh/pandas-dev/pandas/pull/25009/diff?src=pr&el=tree#diff-cGFuZGFzL3RzZXJpZXMvcGxvdHRpbmcucHk=) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/tseries/converter.py](https://codecov.io/gh/pandas-dev/pandas/pull/25009/diff?src=pr&el=tree#diff-cGFuZGFzL3RzZXJpZXMvY29udmVydGVyLnB5) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/io/formats/html.py](https://codecov.io/gh/pandas-dev/pandas/pull/25009/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2Zvcm1hdHMvaHRtbC5weQ==) | `0% <0%> (-99.35%)` | :arrow_down: |
| [pandas/core/groupby/categorical.py](https://codecov.io/gh/pandas-dev/pandas/pull/25009/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZ3JvdXBieS9jYXRlZ29yaWNhbC5weQ==) | `0% <0%> (-95.46%)` | :arrow_down: |
| [pandas/io/sas/sas7bdat.py](https://codecov.io/gh/pandas-dev/pandas/pull/25009/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL3Nhcy9zYXM3YmRhdC5weQ==) | `0% <0%> (-91.17%)` | :arrow_down: |
| [pandas/io/sas/sas\_xport.py](https://codecov.io/gh/pandas-dev/pandas/pull/25009/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL3Nhcy9zYXNfeHBvcnQucHk=) | `0% <0%> (-90.15%)` | :arrow_down: |
| ... and [124 more](https://codecov.io/gh/pandas-dev/pandas/pull/25009/diff?src=pr&el=tree-more) | |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/25009?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/25009?src=pr&el=footer). Last update [abf0824...0e6de81](https://codecov.io/gh/pandas-dev/pandas/pull/25009?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/25009?src=pr&el=h1) Report
> Merging [#25009](https://codecov.io/gh/pandas-dev/pandas/pull/25009?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/9feb3ad92cc0397a04b665803a49299ee7aa1037?src=pr&el=desc) will **decrease** coverage by `<.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/25009/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/25009?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #25009      +/-   ##
==========================================
- Coverage   91.97%   91.96%   -0.01%     
==========================================
  Files         175      175              
  Lines       52368    52365       -3     
==========================================
- Hits        48164    48157       -7     
- Misses       4204     4208       +4
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.52% <100%> (-0.01%)` | :arrow_down: |
| #single | `40.7% <0%> (-0.15%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/25009?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/reshape/merge.py](https://codecov.io/gh/pandas-dev/pandas/pull/25009/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvcmVzaGFwZS9tZXJnZS5weQ==) | `94.45% <100%> (-0.03%)` | :arrow_down: |
| [pandas/io/gbq.py](https://codecov.io/gh/pandas-dev/pandas/pull/25009/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2dicS5weQ==) | `78.94% <0%> (-10.53%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/25009/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `96.9% <0%> (-0.12%)` | :arrow_down: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/25009?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/25009?src=pr&el=footer). Last update [9feb3ad...88cdf8b](https://codecov.io/gh/pandas-dev/pandas/pull/25009?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 @jreback I've modified the logic so the same behavior is used for all dtypes: missing indices are filled with an appropriate NA value can you merge master @jreback done @JustinZhengBC so we are calling this an internal impl change, this has no outward effects? IOW user code will be unchanged? or does this have any cases that now work that didn't? @jreback #24916 had a whatsnew note like "bug in merge when merging by index name would sometimes result in an incorrectly numbered index," which is the same problem this addresses. There is an outwards change in that merge now fills in missing index values with NA values, whereas previously it would try to infer index values based on the other index. I have modified the whatsnew to clarify the new behaviour lgtm. can you merge master; ping on green. @jreback done thanks @JustinZhengBC 