"Promote to existing feature" drop-down can't currently be filtered by product, neither does it allow to identify which product a feature is associated with through its Feature ID prefix (such as "ARCH" or "FREDSLO").
Thank you for your idea. When promoting to an existing feature, you can filter by searching. Searches can include either keywords or the reference number (e.g. starting with the product prefix.) Additionally, the reference number including the product prefix is displayed before the feature summary in the dropdown.