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I have a table with a geometry column (polygon) in a projected coordinate system in meters. Let's say, I want to shift all the polygons by some constant. For example, every point in all polygons must be shifted by X + 4 and Y - 4. Is there a way to do that using PostGIS?

In QGIS, I can do that by selecting all the polygons and using the Move Feature tool. However, QGIS crashes as the amount of vector features is huge, so I try to complete it in PostgreSQL.

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You should use ST_Translate for this intent https://postgis.net/docs/ST_Translate.html

UPDATE your_table
SET your_geom_column_name = ST_Translate(your_geom_column_name, 4, 4);

Be aware 4 are units from your geometry projection. Would be better if meters instead of degrees as 4 degrees something like hundred of kilometres...

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