BUG: `pd.period_range` ignores multiple of `start` frequency.
Fixes: #47465

- [x] closes #47465
- [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).
- [ ] 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.

Hopefully that is fixed now.

@phofl However, during testing I found this behaviour odd:

```py
In [1]: import pandas as pd

In [2]: p = pd.Period("2020", freq="Y")

In [3]: pd.Period(p, freq="3Y")
Out[3]: Period('2020', 'A-DEC')

In [4]: pd.Period(p, freq="3D")
Out[4]: Period('2020-12-31', '3D')
```

The `freq` argument is ignored when the value is already a `Period` and has the same base-freq. I assume this is also not intended? This looks wrong:

https://github.com/pandas-dev/pandas/blob/d9dd1289e07d86928d144e53beb3d5b8ab3c2215/pandas/_libs/tslibs/period.pyx#L2554-L2561

Checking the `_period_dtype_code` should not be sufficient, if the `.n` do not match. This might be deliberate, are there tests covering this? > This might be deliberate, are there tests covering this?

I would be very surprised by this, so let's see: #47613
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