Use the approach in the parent task not just for the main snak of a statement, but also for qualifiers and references.
This will probably need some thought as to how we deal with qualifiers in data types that aren’t supported yet. For main snaks this isn’t really a problem, as we just don’t support opening the edit statement dialog. But what happens if I start editing a string statement with an item qualifier? Ideally I’d still see the qualifier in the edit dialog, but it’s not yet clear what the editStatementsStore should contain in this case.