It's a generated column, so there's no overhead to keep it up to date, but all generated columns in PG are stored. The corpus for text search will be stored 1x

It's a generated column, so there's no overhead to keep it up to date, but all generated columns in PG are stored. The corpus for text search will be stored 1x in the source column, 1x as a tsvector in the index, and an additional 1x in the generated column if you do so. That's a 50% increase in disk space.