An issue (or item) is a discrete single object which belongs to a single project. You can not have it in multiple projects. You can include it in many boards, and hence backlogs, if you want, but as it's a single issue, it won't be "independent" - any changes made by users on one board, or in the issue outside boards, will be reflected in other places, because there is only one item there.
If you need independence, create more issues (there's a clone option that might help)
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