Vlad nanoscrew I'm having the same issue, and this is probably the key part to reproduce it: the language has to be non-English.
The bookmarks folder where favorites are stored (or pseudo-folder, I'm not sure how it works under the hood) is always called Favorites [verbatim in English], no matter what the UI language is.
(By the way, maybe this deserves a separate bug report? The word Favorites should definitely be localized on the front end.)
Anyway, the problem seems to be that if the language for Orion is not English, either due to system settings, or the per-app preference for Orion in particular, the Start Page UI fails to retrieve the actual bookmarks from the Favorites folder. (Possibly because it's looking for the localized term, rather than the English one?)
The bug only happens on iOS. On Mac, while the heading again shows the non-localized, English word "Favorites", they are still indeed shown.
See screenshots below – if the app-specific language for Orion is set to Czech vs. English. The favorites are only missing on iPhone.


