Firstly, 25th Century Federation isn't really covered by Picard, that's more the realm of Star Trek Online... Which is of dubious canon granted, but has contributed more to official canon than most secondary sources have. That said, I also understand why folks tend to prefer the TNG era for setting these scenarios: we have good information on era that is more expansive and easily accessed without having to wade through anywhere near as much garbage.
Secondly... this scenario would utterly destabilize the entire playout of the era... at least until 2387 when they, the Romulans, and probably a large chunk of the Breen get wiped out due to the Hobbus event.
By placing the Blood Angels on the border between the RSE and Federation this means they will no longer have as much contact. This will likely end up preventing the events of Reunification and the eventual softening of Romulan/Federation relations that played out. Further, as other notes, this hostile power, assuming they don't try and conquer Earth thus forcing the Federation into an existential war, will still force the Federation into a major retool of the fleet as well as a major refocus on the Federation core (something a lot of people forget is that the RSE is actually the CLOSEST hostile power to the Federation's core:
As others noted, this likely means the Federation not having the resources to set up on Terok Nor and likely the Cardassians continuing to hold Bajor. Without the Federation taking it over, the Wormhole will not be discovered, and without the Wormhole the Dominion War will not be triggered for another hundred or two-hundred years (as per the Founders original timeline).
What this FURTHER means is there's no thawing of Romulan/Federation relationships due to shared wartime efforts... the Romulans never have a coup that even further weakens them and their central government... and thus...
Spock has no reason, or ability, to intervene with the Hobbus event, thus the propagation wave from that will continue to spread out until it hits Federation space which will use Red Matter to break up the wave as much as possible preserving itself, while the Blood Angels and Romulans are basically completely eliminated by the event as neither has the technology to counteract it.