I had an product discovery idea (idea-1) and needed to move it to a Jira Software Project (company managed). Product Discovery didn't appear to have a "move" function, so I used advanced search, and then 'bulk move' to move it from idea-1 to the Jira Software Project.
I can still access the idea using the original URL:
https://x.atlassian.net/jira/polaris/projects/<discovery project>/ideas/view/123456?selectedIssue=idea-123
(btw, I cannot add comments to it or even archive it). It appears to be a dead end.
Normally, when you move an epic/task etc between projects, and you access the original key, JIRA redirects to you to new key.