Update every selected row
A somewhat complicated way could be
WITH new_users AS (
   UPDATE users SET new = TRUE
   WHERE NOT new RETURNING /* all columns except &quot;new&quot; */
)
 SELECT /* all columns except &quot;new&quot; */
 FROM new_users
UNION
 SELECT /* all columns except &quot;new&quot; */
 FROM users;

The UNION will eliminate duplicates.