这是一个间隙和孤岛问题，您需要将“相邻”行分组在一起。
在这里，我认为最简单的方法是使用行号之间的差异来定义组：

select client_id, event, count(*) cnt, min(time) start_time, max(time) end_time
from (
    select 
        t.*,
        row_number() over(partition by client_id order by time) rn1,
        row_number() over(partition by client_id, event order by time) rn2
    from mytable t
) t
group by client_id, event, rn1 - rn2
order by client_id, min(time)

db小提琴演示：

client_id | event       | cnt | start_time | end_time
:-------- | :---------- | --: | :--------- | :-------
A         | view        |   3 | 12:00:00   | 12:05:00
A         | purchase    |   1 | 14:02:00   | 14:02:00
B         | view        |   3 | 12:04:00   | 13:20:00
C         | view        |   2 | 12:00:00   | 12:07:00
C         | add_to_cart |   1 | 14:02:00   | 14:02:00
C         | view        |   1 | 14:19:00   | 14:19:00
C         | purchase    |   1 | 14:32:00   | 14:32:00
C         | view        |   1 | 15:32:00   | 15:32:00