Hi,
I’m afraid synonyms can’t be extended to the taxonomy term results, they only work for CPTs – as the they are applied to the index table and that only applies to CPT results. I usuall recommend a custom code or a modification where possible, but this is not possible to solve via the index table due to object ID conflicts and missing fields.
The only way around it is to add the additional keywords (synonyms) to term metadata and then enable search for the term meta table.