How can I split a polygon into two equal parts along a N-S axis?

I have a PostGIS database with a table called 'sites' that includes a field sitename and a field geometry.

If I select, e.g.

select sitename, ST_AsGeoJSON(geometry) from sites limit 1;

I get:

Plot 7 | {"type":"Polygon","coordinates": [[[-111.974951718315,33.0745275800293,353], [-111.974935360975,33.0745276003588,353], [-111.974935370263,33.0745546649121,353], [-111.974951727608,33.0745546445826,353],[-111.974951718315,33.0745275800293,353]]]}

These are rectangles oriented very close to N-S. I would like to divide each plot in half along (or close to) its N-S axis. Is there an easy way to do this?

Solutions in PostGIS-SQL preferred. Ultimately I plan to write insert statements like

insert into sites (name, geometry)
values ('Site 1 E', (select ??east half of geometry?? from sites where name = 'Site 1'))

The closest I've gotten is ST_Split, which requires the polygon as well as the 'blade' (line used to split), but it is not clear how I can compute the blade from the geometry.

I would like to divide each plot in half along (or close to) its N-S axis. Is there an easy way to do this? [...] can compute the blade from the geometry.

Something like?

xmin+((xmax-xmin)/2)

Here we create a sample data set foo. In it we create a polygon, we calculate the xaxis to bisect the polygon with, and we create the blade.

Then we do the bisection and display the results with ST_AsText

WITH foo AS (
FROM ST_MakeEnvelope(-10,-10,10,10) AS geom
CROSS JOIN LATERAL ( SELECT ST_xMin(geom) + (ST_xMax(geom) - ST_xMin(geom)) / 2 ) AS axis(x)
CROSS JOIN LATERAL ST_MakeLine(
ST_MakePoint(axis.x, ST_yMin(geom)),
ST_MakePoint(axis.x, ST_yMax(geom))