OpenSearch-compatible search engines which have been added to Firefox are not synced by Firefox Sync. They are conceptually similar to addons and are configured in the Firefox settings, and both addons and settings are synced by Firefox Sync.
I also wish for that feature, especially on mobile devices where setting up the same search wich one already had set uo on al other devices is so much more uncomfortable. This would make life so much easier.
I dont understand why firefox makes it so difficult to add search engines. I usese wikidata a lot, also openstreetmap and openstreetmap wiki. But I have to add theses engings on every client seperately and I always have to tediously figure out where that was hidden and it is so frustrating that it is so difficult in the fist place and that I have to do that all over again for every client even with firefox sync.