Update table with sum from other table for the same id
this should do what you want
update dst
   set counter = dst.counter + src.counter
from src
where src.user_id = dst._user_id;

If dst.user_id is the primary key (or defined as unique), you can combine both into one statement:
insert into dst (user_id, counter, text)
select user_id, counter, text
from src 
on conflict (user_id) 
do update
  set counter = dst.counter + excluded.counter;