It's probably linked to the projection the buffer will use. By default, it will do that:

>  It determines a planar spatial reference system that best fits the bounding box of the geography object (trying UTM, Lambert Azimuthal Equal Area (LAEA) North/South pole, and finally Mercator ). The buffer is computed in the planar space, and then transformed back to WGS84. This may not produce the desired behavior if the input object is much larger than a UTM zone or crosses the dateline 

Your geometry is definitly bigger than an UTM zone, and if you make your buffer in 3857 (mercator) directly you get the same result:

    SELECT
    ST_Buffer(
      st_transform(
        st_setsrid(
          ST_GeomFromtext(
            'linestring(-3.01055556 56.46583333, -71.20583333 46.825)'
          ),
          4326
        ),
        3857
      ),
      999 * 1852,
      'quad_segs=30 endcap=round join=round'
    )

So it mean the ST_buffer fall back to 3857 for your geom. If you want a more correct result for your case, you have to choose a better fitting projection, in your case one that respects the distances instead of the form. For example, there is the [Bonne projection (srid 54024)][1] (there is probably better suited projection for your case, but it's a classic). Replace the 3857 in the request above, and I think the result (in red) is closer to what you expect than the 3857 projection (in green):

[![Differences between the projections][2]][2]


  [1]: https://epsg.io/54024
  [2]: https://i.sstatic.net/lw0Nk.jpg