Postgres 12

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create table test (id serial, value text);
insert into test (value)
select 'test'||generate_series(10,20);
create table test_del_log (id integer, value text, del_date timestamp );

CREATE OR REPLACE FUNCTION prevent_del_trg (
)
RETURNS trigger
    LANGUAGE 'plpgsql'
AS
$body$
BEGIN 
--IF current_user = 'X'  THEN
 INSERT INTO test_del_log
    VALUES (old.*,  now()) ;
--END IF;
COMMIT;

--IF current_user = 'X' THEN
RAISE EXCEPTION 'Delete guard. Access denied for user X';
--ELSE RETURN NEW;
--END IF;

END;
$body$;

CREATE TRIGGER test_prevent_del_trg
    BEFORE DELETE
    ON public.test
    FOR EACH ROW
    EXECUTE PROCEDURE prevent_del_trg();
    
CREATE TABLE

INSERT 0 11

CREATE TABLE

CREATE FUNCTION

CREATE TRIGGER

delete from test where id = 5

ERROR:  invalid transaction termination
CONTEXT:  PL/pgSQL function prevent_del_trg() line 7 at COMMIT

select * from test_del_log

id
value
del_date

SELECT 0