Compute duration of an event based on consecutive values in another column
Here is one idea that you might want to try:
select max(ts) - min(ts)
from (
    select ts, w
       ,   row_number() over (order by ts)
         - row_number() over (partition by w order by ts) as grp
    from test
) as t
where w
group by grp;

The idea is to enumerate ts in two ways, first the complete set, then per w and calculate the difference (called grp).
If the difference (grp) changes it means that w changed. We can, therefore, pick the max(ts) - min(ts) within each grp, for groups where w = true.
The problem you are trying to solve is often referred to as an &quot;island and gap&quot; problem. I modified your fiddle with my query: Modified fiddle
You can try and compare the performance with your function. You probably want to add an index like:
CREATE INDEX x1 on test (ts, w);

EDIT: to calculate the total duration in seconds:
select EXTRACT(EPOCH from sum(dur))
from (
    select max(ts) - min(ts) as dur
    from (
        select ts, w
          ,    row_number() over (order by ts)
            -  row_number() over (partition by w order by ts) as grp
        from test
    ) as t
    where w
    group by grp
) as tt;    

EDIT: I played around a bit more, see Updated fiddle, and added a bit more data (~ 70000 rows depending on the number of duplicates ). I can see that the results differ between queries, haven't examined that more closely though. But I'm a bit surprised that you say that the queries perform about the same. Looking at the plan for your query:
Aggregate  (cost=21650.65..21650.66 rows=1 width=4) (actual time=2389.576..2389.576 rows=1 loops=1)
  -&gt;  Seq Scan on test  (cost=0.00..1190.40 rows=81840 width=9) (actual time=0.013..36.243 rows=68709 loops=1)
Planning Time: 0.097 ms
Execution Time: 2389.663 ms

and one with window functions:
Aggregate  (cost=18951.01..18951.02 rows=1 width=8) (actual time=163.179..163.179 rows=1 loops=1)
  -&gt;  HashAggregate  (cost=18946.01..18948.51 rows=200 width=24) (actual time=160.594..162.306 rows=8447 loops=1)
        Group Key: t.grp
        -&gt;  Subquery Scan on t  (cost=16183.91..18639.11 rows=40920 width=16) (actual time=106.327..146.336 rows=59271 loops=1)
              Filter: t.w
              Rows Removed by Filter: 9438
              -&gt;  WindowAgg  (cost=16183.91..17820.71 rows=81840 width=17) (actual time=106.326..140.013 rows=68709 loops=1)
                    -&gt;  Sort  (cost=16183.91..16388.51 rows=81840 width=17) (actual time=106.316..114.565 rows=68709 loops=1)
                          Sort Key: test.ts
                          Sort Method: external merge  Disk: 2296kB
                          -&gt;  WindowAgg  (cost=7868.76..9505.56 rows=81840 width=17) (actual time=44.285..81.613 rows=68709 loops=1)
                                -&gt;  Sort  (cost=7868.76..8073.36 rows=81840 width=9) (actual time=44.261..52.843 rows=68709 loops=1)
                                      Sort Key: test.w, test.ts
                                      Sort Method: external merge  Disk: 1288kB
                                      -&gt;  Seq Scan on test  (cost=0.00..1190.40 rows=81840 width=9) (actual time=0.011..5.775 rows=68709 loops=1)
Planning Time: 0.224 ms
Execution Time: 164.052 ms

indicate that the latter is significantly more efficient
I'll see if I can spin up a container with Postgres and dump the data into a table and examine the different results
The index is probably not that useful since we are scanning the whole table anyhow.
Final edit:
I could repeat the diff with only 50 rows Fiddle, so I added the rows to a Libreoffice Calc sheet. It appears as if the window version and Libreoffice agrees on the result. For some reason, I got a negative number from your function. This may be due to that the first row is a single row. This is the data used in verification, perhaps you can just add a &quot;t&quot; row a couple of seconds before the first one to rule out errors due to a single row:
2020-07-27 15:55:37 t
2020-07-27 16:01:56 f
2020-07-27 16:09:17 t
2020-07-27 16:23:32 t
2020-07-27 16:28:47 t   00:19:30
2020-07-27 18:14:32 f
2020-07-27 18:30:26 t
2020-07-27 18:40:52 t
2020-07-27 19:01:18 t
2020-07-27 19:05:24 t
2020-07-27 19:16:16 t
2020-07-27 19:56:00 t
2020-07-27 20:34:05 t   02:03:39
2020-07-27 21:12:18 f
2020-07-27 21:58:53 t
2020-07-27 23:51:55 t
2020-07-28 00:42:24 t
2020-07-28 00:43:56 t
2020-07-28 01:15:08 t
2020-07-28 03:34:08 t
2020-07-28 06:20:28 t
2020-07-28 06:23:14 t
2020-07-28 06:30:51 t
2020-07-28 06:34:12 t
2020-07-28 06:38:41 t
2020-07-28 06:48:48 t
2020-07-28 07:49:39 t
2020-07-28 08:28:41 t
2020-07-28 09:32:42 t
2020-07-28 09:45:36 t
2020-07-28 09:57:46 t
2020-07-28 10:29:37 t
2020-07-28 11:53:21 t
2020-07-28 11:53:29 t
2020-07-28 11:54:35 t
2020-07-28 12:23:18 t
2020-07-28 13:10:48 t
2020-07-28 13:37:21 t
2020-07-28 14:22:14 t
2020-07-28 14:51:16 t
2020-07-28 14:52:12 t
2020-07-28 15:30:04 t
2020-07-28 16:34:43 t
2020-07-28 17:02:03 t   19:03:10
2020-07-28 18:11:49 f
2020-07-28 18:21:09 t
2020-07-28 18:41:38 t
2020-07-28 19:14:45 t
2020-07-28 19:16:01 t
2020-07-28 19:22:03 t   01:00:54

             Total      22:27:13        80833 seconds

Final edit 2:-)
I had a look at your function, and it appears as if you expect the rows to be ordered according to ts? If so, that is a false assumption since they may come in any order. If you do a simple test like:
SELECT ddur(ts, w) FROM (select ts, w from test order by random()) as t;

and compare with:
SELECT ddur(ts, w) FROM test;

the results are probably different. See Modified original Fiddle