Visualize PostGIS geography bounding boxes to understand the "&&" operator

Geography use great circle arcs instead of straight lines. To visualize them, you can segmentize a geography into small segments, then convert these segments to geometry

WITH src(geom) AS (SELECT ST_MakeEnvelope(-130.0, 30.0, -129.0, 31.0, 4326) AS geom)
SELECT
    st_segmentize(geom::geography,1000)::geometry
FROM src;

That being said, a great circle along a meridian is the meridian itself, so I really fail to see why the geography bounding box are said to overlap. If it fits your workflow, using st_intersects() will return false with the two sample shapes as geography.