Language tags as defined in BCP 47 (currently RFC 5646) do not specify any codes for informal vs. formal variants of German. It would probably be unrealistic to try to have such codes registered, so you would be limited to Private Use subtags, e.g. de-x-formal vs. de-x-informal. Whether your software can handle these in any way is a different issue.
On the practical side. the choice of “Sie” vs. “Du” (or “du”) is hardly a language variant issue. Standard German uses both pronouns to address a person in singular, depending on style of presentation and on the relationship with the addressed person. At the extreme, we could say that the choice of “Sie” vs. “Du” in the context of addressing a user generically in instructions or a user interface is a language variant issue. But on the practical side, just make up your mind.