Assuming the new ID is a text-based data type, e.g., Single-Line Text…
Do a toolbar search for Zettel-ID is not, leaving the text field empty, so it matches items with a value for the attribute.
Select the search results, then choose Tools > Batch Process and set it up like so…
In the first field, Control-click > Insert Placeholder > Custom Metadata > Zettel-ID.
In the second field, just leave the text field empty to clear the Zettel-ID after the change.
Simple and no scripting involved!