Filling in gaps between polygons using PostGIS functions

I have a similar question to Filling gaps between polygons using QGIS

The solution talks about using it in QGIS but I want to use PostGIS functions on a table on the geometry column.

The solution talks about convex hull but not sure how to use the convex_hull PostGIS function here. I want to fill the gap by moving/merging the gap to the neighboring polygon.