this task is a gap and island problem. The queries I provided couldn't give me correct session_id, but first_ts is correct. I need help to make the query work in correct way.

Here is the modified version:
-- create temp table with lagged columns
create temp table lags as

select *,
lag(webid, 1, webid) over(partition by userid order by ts) as lag_webid,
lag(ts, 1, ts) over(partition by userid order by ts) as lag_ts
from mytable;
-- identify session...