The manual says postgres only supports materialized (ie, stored) generated columns, which means the value is generated when the row is inserted or updated, which means it will use the insert/update date, not the CURRENT_DATE you want.
So, you need to create a view instead. This allows evaluating CURRENT_DATE at the date of the SELECT, not the INSERT/UPDATE, to generate columns.
CREATE VIEW foo AS SELECT *,
(CURRENT_DATE - public.gantt_Tasks.start_date)
/ (public.gantt_Tasks.end_date-public.gantt_Tasks.start_date)
AS percentage_progress
FROM public.gantt_task
Note DATEDIFF is mysql syntax not postgres, and division by zero is not allowed, so if start_date and end_date can be identical then you'll have to modify the expression conditions depending on what you want. Also your expression will go over 100% when CURRENT_DATE is later than end_date. Perhaps something like:
least( 1.0, (CURRENT_DATE-start_date)/greatest( 1, end_date-start_date)::FLOAT )