sqlite update each row of a column with the result of a select (again)

I need to add a column to a table then fill it with computed values from a select (from the orignal table itself) like this

create table yo (ad integer primary key, pa integer, pd integer);
insert into yo values
  (1,1,1),(2,1,3),(3,1,4),(4,3,5),(5,4,2),(6,3,8),(7,1,9),(8,6,7),(9,3,6);
.header on
.mode column yo;
select * from yo;
ad          pa          pd
----------  ----------  ----------
1           1           1
2           1           3
3           1           4
4           3           5
5           4           2
6           3           8
7           1           9
8           6           7
9           3           6

The 'ad' col is a kinda address, the 'pa' col is a parent address, the 'pd' col is a kinda ID or value for that row. I'd like to add a col named 'pp' that would be a 'parent ID' that would be computed like this

select yo2.pd from yo yo1 join yo yo2 on yo2.ad=yo1.pa;
pd
----------
1
1
1
4
5
4
1
8
4

So I'd like to setup 'pp' whit this output I tried this but obviously I must miss somethings

alter table yo add column pp integer;
update yo set pp =
  (select yo2.pd as pp from yo yo1 join yo yo2 on yo2.ad=yo1.pa);

ad    pa   pd   pp
----  ---  ---  ---- 
1     1    1    1
2     1    3    1
3     1    4    1
4     3    5    1
5     4    2    1
6     3    8    1
7     1    9    1
8     6    7    1
9     3    6    1

Does what I want to achieve is doable, I so othre link on similar proble that I don't understand the answers, and I found also tiny case like this

create table t1 (a int, b int);
insert into t1 values (1,0),(2,0);
create table t2 (a int, c int);
insert into t2 values (1,101),(2,102);
update t1 set b = (select c from t2 where t2.a = t1.a) where t1.b = 0;

This one do update correctly so why my select differ from this later one?
Thanx for any advise
Phi