CLN: Remove StringMixin from pandas.core.computation
- [x] xref #25725
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`

StringMixin is not really useful anymore and only functions to reverse the calling order of ``__str__`` and ``__repr__``, which is now not-standard in Python3.

This removes the usage of StringMixin in pandas.core.computation. Followups will remove the class from other modules.

# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/26482?src=pr&el=h1) Report
> Merging [#26482](https://codecov.io/gh/pandas-dev/pandas/pull/26482?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/d3a19121790a517c03755fc01f74ab149d9c77f5?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/26482/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/26482?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #26482      +/-   ##
==========================================
- Coverage   91.75%   91.74%   -0.01%     
==========================================
  Files         174      174              
  Lines       50756    50731      -25     
==========================================
- Hits        46572    46544      -28     
- Misses       4184     4187       +3
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.26% <100%> (ø)` | :arrow_up: |
| #single | `41.68% <100%> (-0.1%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/26482?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/computation/pytables.py](https://codecov.io/gh/pandas-dev/pandas/pull/26482/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29tcHV0YXRpb24vcHl0YWJsZXMucHk=) | `90.28% <100%> (+0.03%)` | :arrow_up: |
| [pandas/core/computation/ops.py](https://codecov.io/gh/pandas-dev/pandas/pull/26482/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29tcHV0YXRpb24vb3BzLnB5) | `95.75% <100%> (-0.21%)` | :arrow_down: |
| [pandas/core/computation/expr.py](https://codecov.io/gh/pandas-dev/pandas/pull/26482/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29tcHV0YXRpb24vZXhwci5weQ==) | `97.5% <100%> (-0.03%)` | :arrow_down: |
| [pandas/io/gbq.py](https://codecov.io/gh/pandas-dev/pandas/pull/26482/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/26482/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.02% <0%> (-0.12%)` | :arrow_down: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/26482?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/26482?src=pr&el=footer). Last update [d3a1912...29e3e45](https://codecov.io/gh/pandas-dev/pandas/pull/26482?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/26482?src=pr&el=h1) Report
> Merging [#26482](https://codecov.io/gh/pandas-dev/pandas/pull/26482?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/d3a19121790a517c03755fc01f74ab149d9c77f5?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/26482/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/26482?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #26482      +/-   ##
==========================================
- Coverage   91.75%   91.74%   -0.01%     
==========================================
  Files         174      174              
  Lines       50756    50731      -25     
==========================================
- Hits        46572    46544      -28     
- Misses       4184     4187       +3
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.26% <100%> (ø)` | :arrow_up: |
| #single | `41.68% <100%> (-0.1%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/26482?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/computation/pytables.py](https://codecov.io/gh/pandas-dev/pandas/pull/26482/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29tcHV0YXRpb24vcHl0YWJsZXMucHk=) | `90.28% <100%> (+0.03%)` | :arrow_up: |
| [pandas/core/computation/ops.py](https://codecov.io/gh/pandas-dev/pandas/pull/26482/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29tcHV0YXRpb24vb3BzLnB5) | `95.75% <100%> (-0.21%)` | :arrow_down: |
| [pandas/core/computation/expr.py](https://codecov.io/gh/pandas-dev/pandas/pull/26482/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29tcHV0YXRpb24vZXhwci5weQ==) | `97.5% <100%> (-0.03%)` | :arrow_down: |
| [pandas/io/gbq.py](https://codecov.io/gh/pandas-dev/pandas/pull/26482/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/26482/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.02% <0%> (-0.12%)` | :arrow_down: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/26482?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/26482?src=pr&el=footer). Last update [d3a1912...29e3e45](https://codecov.io/gh/pandas-dev/pandas/pull/26482?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
