REGR: fix eval with inplace=True to correctly update column values inplace
- [x] closes #47449
- [x] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [x] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [x] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

The bad commit that causes this issue (see https://github.com/pandas-dev/pandas/pull/43406) is the rootcause for multiple others, so am not sure if we want to tackle the overall problem bit by bit or if there is a generic solution to all of them.
Hello @CloseChoice! Thanks for updating this PR. We checked the lines you've touched for [PEP 8](https://www.python.org/dev/peps/pep-0008) issues, and found:





There are currently no PEP 8 issues detected in this Pull Request. Cheers! :beers: 

##### Comment last updated at 2022-08-19 08:09:31 UTC Could you add a whatsnew? Is there a suitable class for this test?

The root cause was intended, so we have to fix them where they occur.  > Could you add a whatsnew? Is there a suitable class for this test?
> 
> The root cause was intended, so we have to fix them where they occur.

Thanks for the answer. I added a whatsnew entry. @CloseChoice I started converting the suggestion at https://github.com/pandas-dev/pandas/issues/47449#issuecomment-1180701954 into a PR, missing that you already opened one with a very similar fix! I hope you don't mind, but so I merged some of the changes I started doing in your PR:

- Also checking for `inplace` in eval.py (when not doing inplace, I think the `target[assigner] = ret` without loc is faster), as suggested in https://github.com/pandas-dev/pandas/issues/47449#issuecomment-1180701954). In addition I also replaced (Series, DataFrame) with NDFrame
- I slightly updated the test (used some simpler (less) values), and also added a check for a viewing Series to be updated (in addition to viewing DataFrame) Is it possible to get there with a MultiIndex? Similar to https://github.com/pandas-dev/pandas/pull/47774 where the dimension reduction bothers us I am not sure if `eval` supports referring (or assigning) to MultiIndex columns (I also don't directly see a test in `test_eval.py` that involved MultiIndex). I tried a few things that all fail:

```
# those two give syntax error when parsing the ast
df.eval("('A', 'a') = ('A', 'b') + ('B', 'a')")
df.eval("\"('A', 'a')\" = \"('A', 'b')\" + \"('B', 'a')\"")
# those two each give another error
df.eval("D = ('A', 'b') + ('B', 'a')") 
df.eval("D = \"('A', 'b')\" + \"('B', 'a')\"")
```

If not using existing column names, but just assigning a new column, that still seems to work with this PR:

```
In [1]: df = DataFrame({("A", "a"): [1, 2, 3], ("A", "b"): [4, 5, 6], ("B", "a"): [7, 8, 9]})

In [2]: df
Out[2]: 
   A     B
   a  b  a
0  1  4  7
1  2  5  8
2  3  6  9

In [3]: df.eval("D = 1")
Out[3]: 
   A     B  D
   a  b  a   
0  1  4  7  1
1  2  5  8  1
2  3  6  9  1

In [4]: df.eval("E = 1", inplace=True)

In [5]: df
Out[5]: 
   A     B  E
   a  b  a   
0  1  4  7  1
1  2  5  8  1
2  3  6  9  1
``` Thanks for checking @jorisvandenbossche I don't mind at all. Thanks for picking this up and improving upon it. Greenish, merging thx @CloseChoice  Owee, I'm MrMeeseeks, Look at me.

There seem to be a conflict, please backport manually. Here are approximate instructions:

1. Checkout backport branch and update it.

```
git checkout 1.4.x
git pull
```

2. Cherry pick the first parent branch of the this PR on top of the older branch:
```
git cherry-pick -x -m1 838b04f09fd1cbac2e2ff9307941da6f47c8b792
```

3. You will likely have some merge/cherry-pick conflict here, fix them and commit:

```
git commit -am 'Backport PR #47550: REGR: fix eval with inplace=True to correctly update column values inplace'
```

4. Push to a named branch:

```
git push YOURFORK 1.4.x:auto-backport-of-pr-47550-on-1.4.x
```

5. Create a PR against branch 1.4.x, I would have named this PR:

> "Backport PR #47550 on branch 1.4.x (REGR: fix eval with inplace=True to correctly update column values inplace)"

And apply the correct labels and milestones.

Congratulations — you did some good work! Hopefully your backport PR will be tested by the continuous integration and merged soon!

Remember to remove the `Still Needs Manual Backport` label once the PR gets merged.

If these instructions are inaccurate, feel free to [suggest an improvement](https://github.com/MeeseeksBox/MeeseeksDev).
                