Is it somehow possible to declare the $arduino object as shared, so the garba collection avoids it?

Not directly no. Each thread gets its own copy (actually not a fully copy, but a proxy to the real thing) of each shared variable; and that proxy is local to the thread and must be destroyed before the thread ends. In many cases, the appropriate action is to do nothing in the destroy unless this is the last copy of the handle.

In theory, there is a mechanism whereby module authors can make their modules thread-aware and possible thread-safe, by taking control of the cloning process by defining sub CLONE{ .. } in their packages; but the mechanism is barely described and I've never seen an example of anyone using it; so I cannot comment further on it. Besides which you'd either have to get the author of D::SP interested; or make your own changes.