If a post is deleted from an instance, how long should I expect other instances to completely purge the post.
Of course, I wouldn’t expect anything published in the internet to be completely removed. That’s how an internet is.
Depends how long the federation takes between instances, but generally immediately, providing the other instances are still federated.
That being said, if defederated, the deletion is not federated to the other instances and will stay cached on other instances. This is a bit of an edge case though.
Basically as fast/slow as federation of anything else (posts, comments, votes, etc.) is… on a large instance with lots of load and in a community with lots of subscribers it may take a while to let everyone know, and not everyone will be online so there may be retries and such.
And you are entirely correct about the internet being forever, the “delete” message sent just basically says “the user has chosen to delete this” it is up to the receiving server whether they do so or not.
