Postgres 12

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SELECT 10

with t as (
      select uid, date_trunc('day', session_start_time) as s_day, 1 as inc
      from users_sessions
      union all
      select uid, date_trunc('day', session_start_time) + interval '31 day' as s_day, -1
      from users_sessions
     ),
     tt as (  -- increment the ins and outs to determine whether a uid is in or out on a given day
      select uid, s_day, sum(inc) as day_inc,
             sum(sum(inc)) over (partition by uid order by s_day rows between unbounded preceding and current row) as running_inc
      from t
      group by uid, s_day
     ),
     ttt as (  -- find the beginning and end of the islands
      select tt.uid, tt.s_day,
             (case when running_inc > 0 then 1 else -1 end) as in_island
      from (select tt.*,
                   lag(running_inc) over (partition by uid order by s_day) as prev_running_inc,
                   lead(running_inc) over (partition by uid order by s_day) as next_running_inc
            from tt
           ) tt
      where running_inc > 0 and (prev_running_inc = 0 or prev_running_inc is null) or
            running_inc = 0 and (next_running_inc > 0 or next_running_inc is null)
     )
select s_day,
       sum(sum(in_island)) over (order by s_day rows between unbounded preceding and current row) as active_30
from ttt
group by s_day;

s_day	active_30
2020-01-13 00:00:00	2
2020-01-18 00:00:00	3
2020-02-13 00:00:00	1
2020-02-18 00:00:00	0
2020-03-06 00:00:00	2
2020-03-31 00:00:00	3
2020-04-06 00:00:00	1
2020-05-01 00:00:00	0
2020-08-28 00:00:00	3
2020-09-28 00:00:00	0

SELECT 10