Group multiple events for ID in postgreSQL data

I’m trying to select pairs of events from my data. I have a data that looks like this:

create table test(id,status,created)as values
 (1, 'on','2024-09-01'::date)
,(2, 'on','2024-09-02'::date)
,(1,'off','2024-09-03'::date)
,(1, 'on','2024-09-04'::date)
,(2,'off','2024-09-05'::date)
,(3, 'on','2024-09-06'::date)
,(1,'off','2024-09-07'::date)
,(4,'off','2024-09-08'::date);

I would like to have data like this:

I am interested in:

1. multiple events for the same id in the data
2. null values when either end of event pair is missing

>Solution :

An example using the self-join:

1. Match on id
2. Make sure the left table is for earlier on events, right for later off.
3. This matches every on event with all later offs for each id. A distinct on keeps only a single match for each id and on event, selecting the soonest off.

_{demo at db<>fiddle}

select distinct on (1,2)
       coalesce(t1.id,t2.id)
      ,t1.created as switched_on 
      ,t2.created as switched_off
from test as t1 
full join test as t2 
       on t1.id=t2.id 
      and t1.created<t2.created
where coalesce(t1.status,'on')='on' 
  and coalesce(t2.status,'off')='off'
order by 1,2, t2.created-t1.created;