As you said, GET /resolove_object
(https://join-lemmy.org/api/interfaces/ResolveObject.html) may work:
$ post_id=9589178
$ curl 'https://lemm.ee/api/v3/resolve_object?q=https%3A%2F%2Fprogramming.dev%2Fpost%2F${post_id}' | jq .post.post.id
22873872
$ curl 'https://lemm.ee/api/v3/post?id=22873872' | jq '.post_view.post | [.id, .name]'
[
22873872,
"How do you get the url or id of the same post on a different instance?"
]