Recursive count query in PostgreSQL

I have a website on which users can place comments on nodes and also comment as a reply to other comments without a depth limit. The table structure of the comments table is as follows (simplified):

The nodes themselves are not part of this table. The visualized hierarchical structure of the data above is

node with id 1
 |- (cid: 1) initial comment on node with id 1
 |   |- (cid: 2) reply to comment with id 1
 |   |   |- (cid: 3) reply to comment with id 2
 |   |- (cid: 4) second reply on first comment
 |- (cid: 6) second direct child comment on node 1
node with id 2
 |- (cid: 5) comment on another node
node with id 3
 |- (cid: 7) comment on a third node
 

So, effectively, the columns "entity_type" and "entity_id" in unison identify the entity that the comment belongs to.

Now I would like to run a sql query that returns me the node ids (!) and the number on comments on these nodes of nodes which ids are given - so something like this, when only nodes with the id 1 and 2 are of interest:

I tried multiple versions of recursive queries (all using the "with recursive x as..." syntax), but for the life of me I am seemingly unable to form the correct one. Any help would be greatly appreciated...

Thanks for taking the time to read and have a great day!

Looks like you want

with recursive cte as (
  select entity_id, cid
  from foo
  where entity_type='node'

  union all

  select cte.entity_id, foo.cid
  from cte 
  join foo on foo.entity_type='comment' and foo.entity_id = cte.cid
) 
select entity_id,  count(*) "#comments"
from cte
where entity_id in (1,2)
group by entity_id

db<>foddle