How to insert a value using postgres trigger and function in supabase?

Since you didn't show the user / todo tables, we can only suppose.

Attention to Postgres CREATE TRIGGER::

CREATE [ OR REPLACE ] [ CONSTRAINT ] TRIGGER name { BEFORE | AFTER | INSTEAD OF } { event [ OR ... ] }
    ON table_name
    [ FROM referenced_table_name ]
    [ NOT DEFERRABLE | [ DEFERRABLE ] [ INITIALLY IMMEDIATE | INITIALLY DEFERRED ] ]
    [ REFERENCING { { OLD | NEW } TABLE [ AS ] transition_relation_name } [ ... ] ]
    [ FOR [ EACH ] { ROW | STATEMENT } ]
    [ WHEN ( condition ) ]
    EXECUTE { FUNCTION | PROCEDURE } function_name ( arguments )

Lookout for :

referencing new table as NEW

Try out this example and see if it suits you. Your mileage may vary.

-- newtable definition

-- DROP table created_todos ;
-- drop table TODO;

-- drop function f_updateTodoCounts;
-- drop function f_insertTodoCounts;

CREATE TABLE todo (
    u_created_by integer not null,
    todowhat integer not null,
    primary key( u_created_by, todowhat ) 
);


CREATE TABLE created_todos (
    u_created_by integer ,
    num_of_todos integer ,
    primary key ( u_created_by )
);


create function f_insertTodoCounts() returns trigger
as $f_insertTodoCounts$
declare 
   u_cb INTEGER;
   
begin
    
    select count(td.*) 
    into u_cb 
    from created_todos td , new N
    where N.u_created_by = td.u_created_by;
    
    if u_cb < 1 then 
        insert into created_todos
        select I.u_created_by ,1
        from NEW I;
    else
        update created_todos CT
        set num_of_todos = cnt_todos
        from ( select count(T.todowhat) cnt_todos, T.u_created_by
            from todo T  
            group by T.u_created_by) TD
        where TD.u_created_by = CT.u_created_by
;
    end if;
    return new;
end;
$f_insertTodoCounts$ language plpgsql;

create function f_updateTodoCounts() returns trigger
as $f_updateTodoCounts$
begin
    update created_todos CT
        set num_of_todos = cnt_todos
    from ( select count(1) cnt_todos, u_created_by
            from todo T inner join NEW I on (I.u_created_by = T.u_created_by) ) TD
    where TD.u_created_by = CT.u_created_by;
    return new;
end;
$f_updateTodoCounts$ language plpgsql;


create trigger insTodoCounts
   after insert on todo
   referencing new table as NEW
   for each row 
   execute function f_insertTodoCounts();

create trigger updTodoCounts
   after update on todo
   referencing new table as NEW
   for each row
   execute function  f_updateTodoCounts();
  
insert into todo values ( 1 ,1 );
insert into todo values (2,1 );
insert into todo values (1,2);
insert into todo values (1,3);
insert into todo values  (1,4);
insert into todo values  (1,5);
insert into todo values  (1,6);
insert into todo values  (2,5);
insert into todo values  (3,5);
insert into todo values  (4,7);

select * from created_todos;