It would be nice if I would not have to set up all my search engines and their short codes with every new installation but could sync them just like my add-ons and history.
I agree. Its' really sad that on 2024 sync doesn't include more user settings (search engine, toolbar, theme, layout, add-ons, ecc...). There are multiple aged trending ideas about this (in addition to this one):
This would be really helpful, because copy-pasting all the search engines to my Android phone is annoying. A simple json import/export feature would even suffice.