Gaia results have offset from website

I would like to obtain information from Gaia using an identifier.
The result I get is different to the one from the website. Why?

```
from astroquery.gaia import Gaia
w = u.Quantity(0.001, u.deg)
r = Gaia.query_object('Proxima Centauri', width=w, height=w)
print(r['source_id'])
```
Yields one source with ID 5853498678802473344. It is the wrong source, offset by a few arcsec.

When I use the [Gaia website](https://gea.esac.esa.int/archive/) and enter "Proxima Centauri" into the field "name", I get the source ID 5853498713160606720. This is the correct ID as verified by the parallax.

The problem appears to be strongest for high proper motion objects. Perhaps the lookup for the name "Proxima Centauri" uses some other source, perhaps from Simbad, valid for a different epoch than the one for Gaia?

Start by reproducing the Gaia.query_object example for Proxima Centauri and comparing its source ID and parallax with the Gaia website result. Trace how the name is resolved and how the query position is handled for high-proper-motion objects, including the suspected epoch difference. Done means the discrepancy is corrected or its cause and expected behavior are documented.

Written by the indexing model from the issue text.