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?"
]

Not sure if this is still the case, but a lot of the instances had overcrowding issues. As long as two instances are federated, it makes the most sense to link to the instance that has more available capacity for new users.

That, and a lot of the stuff I follow is on servers that are likely to be de-federated(.ml) or defederate eachother(.ml vs anarchists or primitivists). I prefer to give potential new users the chance to fly under the radar, and only potentially end up banned from a given instance for their own actions. Sharing threads mirrored on more generic instances suits my purposes.

All that said, I'm leaving this thread open, because while I occassionally go to the instance that originated a given thread, scroll to it in their feed, and share the link I find there(there are some niche instances I believe are best for appealing to non-lemmy users who are avid about that niche), that's a PITA non-solution.