Generating rectangle centered by point in QGIS

Check "Rectangles, Ovals, Diamonds (Variable)" geoalgorithm in the QGIS's Toolbox

There is "Geometry by Expression" tool. You should use in a projected coordinate system.

• Select "Polygon" as "Output geometry type" option.

• Click "Expression" button (highlighted blue square)

• And paste the following expression

  make_rectangle_3points(
    make_point($x + "height"/2, $y + "width"/2),
    make_point($x - "height"/2, $y + "width"/2),
    make_point($x - "height"/2, $y - "width"/2)
  )
  

Result: