Unfortunately, you are not missing anything. Currently, there is no method to bulk upload synonyms through WorkBench; they need to be set up one by one via the tree interface. Updating Taxon records individually through SQL or the API is feasible but more complex and risky compared to using the user interface.
This has been requested a number of times and I’ve added your comment to the official issue tracking. If you have more comments or want to share your ideal workflow once this request is implemented, please reply to this topic below or on GitHub!