DOC: building page for nested methods doesn't work
closes #46804 

Like this
```
 python make.py clean && python make.py --single pandas.Series.str.rsplit
```
and
```
 python make.py clean && python make.py --single pandas.Series.value_counts
```
and
```
 python make.py clean && python make.py --single pandas.Series
```
have their docs built fine

cc @jorisvandenbossche 

I didn't find any tests for building docs - are they just tested manually?
So this works locally for you? (Doc build passed which is promising) Yup, worked for a contributor too 

I'll see if I can put a quick check for this together > Doc build passed which is promising

Building with `--single` wasn't previous tested though, so it would've passed anyway :smile:  Have added a quick check for it to the doc build job Very nice! Thanks @MarcoGorelli  @MarcoGorelli - running the code_checks locally, I now get some docs opening up in my browser:

https://github.com/pandas-dev/pandas/blob/c5610d22eda24b7cd8987972d4c2fe9b1a661780/doc/make.py#L236-L242

I don't think this was intentional, right? No much of an issue, more of an oddity. Could we add an argument, e.g. ``--open-browser`` that when unspecified gives current behavior and when specified overrides? Then we could do ``open-browser=False`` in the code checks. Hey @rhshadrach 

> I don't think this was intentional, right?

that's right

how about
```
    argparser.add_argument(
        "--no-browser", help="Don't open browser", action="store_true"
    )
```
which, if passed, won't open the browser, and if not passed, retains the current behaviour?