PostgreSQL ltree: Get all entries and the ancestors in ltree from another table

Question

Tree table

node_Id	tree_path::ltree
aaaa	aaaa
bbbb	aaaa . bbbb
cccc	aaaa . bbbb . cccc
dddd	aaaa . bbbb . dddd
eeee	eeee
ffff	eeee . ffff

Object table

object_id	node_id_fk	name	type
1111	aaaa	name1	node
2222	aaaa	name2	node
3333	cccc	name3	node
4444	dddd	name4	node
5555	eeee	name4	node
6666	eeee	name6	node
7777	bbbb	name7	node
8888	dddd	name8	node
9999	dddd	name9	node

What I want to achieve in two steps:

1. Get all entries from the "Object table" for requested node_ids and all ancestor ids in the tree_path in the "Tree table".
2. And then add a column requested_node_id to to response from (1) to show the requested node_id to the "Object table" entries.

For the 1. step, i think, the the query looks something like that

Only the duplicate entries are not shown.

So we get these entries for the requested nodeIds ('bbbb', 'dddd') from the "Object table"

object_id	node_id_fk	name	type
1111	aaaa	name1	node
2222	aaaa	name2	node
7777	bbbb	name7	node
1111	aaaa	name1	node
2222	aaaa	name2	node
4444	dddd	name4	node
7777	bbbb	name7	node
8888	dddd	name8	node
9999	dddd	name9	node

For the 2. step (show column with the requested node_Id) I don't know how the query :( the response should look like this:

object_id	node_id_fk	name	type	requested_node_id
1111	aaaa	name1	node	bbbb
2222	aaaa	name2	node	bbbb
7777	bbbb	name7	node	bbbb
1111	aaaa	name1	node	dddd
2222	aaaa	name2	node	dddd
4444	dddd	name4	node	dddd
7777	bbbb	name7	node	dddd
8888	dddd	name8	node	dddd
9999	dddd	name9	node	dddd

Unfortunately only shows the node_id from the "node table" and not the requested node id

I hope the question is clear, leet me know if not