Do search engines get synced on Firefox?

Does anyone know if the search engines we add to Firefox get synced and can then be recovered on a reinstall or new profile?

The search engines I’m referring to are the ones glued and associated to the location bar (i.e. URL bar) or MEGA bar as Mozilla has decided to call it now (stupid, I know).

If you do not separate the search capability via the older search bar and the location bar, these are the same things.

I’d rather not have to be visiting every search engine I have saved just to recover them on a fresh profile/install.