BUG: to_numeric str to float has missing digit precision
### 

- [X] I have checked that this issue has not already been reported.

- [X] I have confirmed this bug exists on the [latest version](https://pandas.pydata.org/docs/whatsnew/index.html) of pandas.

- [X] I have confirmed this bug exists on the master branch of pandas.


### Reproducible Example

```python
import pandas as pd
pd.set_option("display.precision", 20)
df = pd.DataFrame(data=["0.01234567890123456789", "0.00498124967521367"], columns=["string"])
df["float"] = pd.to_numeric(df["string"])
df.head()
```


### Issue Description

The conversion to string shall at least return a precision of 17 digits after decimal point.
The first number exceeds voluntarily the maximum precision of 17 digits allowed by FLOAT64 representation. The second number has exactly 17 digits

### Expected Behavior

In 1.1.5 version, output:
```
                   string                   float
0  0.01234567890123456789  0.01234567890123457017
1     0.00498124967521367  0.00498124967521367066
```

When 1.2.0 version (and further versions) outputs:
```
                   string                   float
0  0.01234567890123456789  0.01234567890123450078
1     0.00498124967521367  0.00498124967521360040
```
I think the behaviour fro 1.1.5 should be the right one, keeping a 17 digits precision while converting string to float.

### Installed Versions

<details>

INSTALLED VERSIONS
------------------
commit           : 945c9ed766a61c7d2c0a7cbb251b6edebf9cb7d5
python           : 3.8.11.final.0
python-bits      : 64
OS               : Linux
OS-release       : 3.10.0-693.el7.x86_64
Version          : #1 SMP Tue Aug 22 21:09:27 UTC 2017
machine          : x86_64
processor        : x86_64
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.3.4
numpy            : 1.19.5
pytz             : 2021.3
dateutil         : 2.8.2
pip              : 21.3
setuptools       : 58.2.0
Cython           : 0.29.24
pytest           : 6.1.2
hypothesis       : None
sphinx           : 4.2.0
blosc            : None
feather          : None
xlsxwriter       : 3.0.1
lxml.etree       : 4.6.3
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : 3.0.2
IPython          : 7.28.0
pandas_datareader: None
bs4              : None
bottleneck       : None
fsspec           : 2021.10.1
fastparquet      : None
gcsfs            : None
matplotlib       : 3.4.3
numexpr          : 2.7.3
odfpy            : None
openpyxl         : 3.0.9
pandas_gbq       : None
pyarrow          : 5.0.0
pyxlsb           : None
s3fs             : None
scipy            : 1.7.1
sqlalchemy       : 1.4.25
tables           : 3.6.1
tabulate         : 0.8.9
xarray           : 0.19.0
xlrd             : 2.0.1
xlwt             : 1.3.0
numba            : 0.54.1

</details>
