News Explorer: https://betamagic.nl/products/newsexplorer.html
Includes iCloud syncing across tvOS, iOS, macOS, and watchOS. That said I Still prefer Reeder with Feedly as the background sync service.
News Explorer will let you keep unread (and/or even read, if you want) items forever. I didn't see in this thread what OS you use, but if you're an iOS/MacOS person, you should look into it: https://betamagic.nl/products/newsexplorer.html I have been using it for a couple of years, and I keep unread items forever and have had no problems with that. I have a small group of feeds that I keep up on all the time and a large set I peruse at my leisure. The main limitation on this would be whatever room you have either on iCloud or locally, but even with... a LOT (north of 1M) of unread items, we're talking about 35GB.
I have corresponded with the developer a few times when I had an issue with a feed and he was very responsive.
Sorry if this isn't helpful because you use a different OS, I hope you find a client with the feature you are looking for.