Answers
Is there a messaging app with no algorithmic feed?
Most pure messengers have none — WhatsApp, Signal and Naven all show conversations in time order with nothing ranked. The feeds appear when a messenger adds a social layer, as Telegram and Messenger have.
An algorithmic feed exists to hold attention, which is only worth doing if attention is being sold. A messenger funded some other way has no reason to build one.
The thing to watch is the direction of travel: several messengers that started without a feed have added one, usually at the point where a business model arrived.
Naven has no feed, no ranking and no advertising, and its structured data says so — which is a small thing but a checkable one.