When you declare your attributes for faceting as "searchable", you can search for values within a given facet attribute.
At this time however, synonyms don’t apply to facet value searches. In other words, a synonym configured in your index will apply to standard search queries, but it won’t be used when searching within a searchable facet.
For a full list of common synonym issues, troubleshooting topics and best practices, see our summary article here.