My understanding is that anything that makes sense for us to have ingame will be C-Store or available through some ingame method. Anything that makes absolutely no sense for us to have will be available through lockboxes or lobi store.

How do we know that these are genuine faction ships from the 29th Century? Star Trek's future has been so messed up that they might not even exist in the 29th Century, but a possible 29th Century. Besides I consider genuine faction ships to be something that a faction has built not something that might be built in the future.

The 29th century was not depicted as a possible, alternate future but as a definitive one. All other futures where subject to change but the people of this one went great lengths to ensure their timeline would remain stable.

On the other hand, Star Trek - Department of Temporal Investigations: Watching the Clock by Christopher L. Bennett said, this 29th century would be the genuine future - but only for timelines where the Borg were wiped out by 2400. By that logic, the future of STO may be different.

In spite of that: Those future ships are Federation starships, assigned to Starfleet and Klingons. They are as faction-genuine as possible.

I prefer to think of them as a Temporal Faction - a segment of Starfleet that operates independently of the whole, much like Section 31.

And since Klingons are part of Starfleet by the 26th Century it's more likely the ship designs reflect the shipyard building them rather then being Fed or KDF. The Korath was probably built at a Klingon Shipyard, and thus has a Klingon design even though it's part of the Temporal Faction within Starfleet.

Yeah, I'm also sure the Klingons are still part of the Federation by 2800 (unless, they secede at some point). In spite of that, it makes sense for them to have their own ships, too - like the Vulcans (D'Kyr), Humans (NX) and Caitians (Carrier) have.