I don't think I have seen any other game or movie with the same kind of Lovecraftian cosmic horror feel that Freespace (especially FS2) had back in the day. Mass Effect 1 maybe, but the later games ruined the Reapers and made them lame.
That might be missing the point of the Reapers in Mass Effect. And I hate it being made in the framing of "ruining".
The comparison to cosmic horror is only ever invited by the statements of Sovereign and Harbinger, with their grandiose proclaimations of being superior to organic sentients. In the story, both times, we are invited to distrust those statements as both come after the revelation of Reaper Indoctrination-mind control, meaning that we are already inclined to mistrust anything they say as self-serving. The proclaimation of being "uncomprehnsible" is just a claim they make about themselves.
Additionally, Indocrination is always framed as an invevitibility in the franchise.
But on a further level, analysing the conflict in the three original Mass Effect-games (which is also reflected in Andromeda, if you read Andromeda as response to the valid criticism of the first Mass Effect-games very "vulgarly ahistoric" approach to said conflict), is not about the Reapers. They qualifiy as the inciting actors in each of the original Mass Effect-Trilogy's games and they are provide the shootable opposition for gameplay, but only in Mass Effect 2 is a Reaper actually the antagonistic party of the conflict in the story - which is the integration of Humanity in the Galactic Community as facilitated by the actions of your Command Shepard.
That is the conflict that also actively measured in each game with your Renegade/Paragon-scores and it resovling each sub-conflict of that is what ultimately gets to you achieving your goals, rather than any confrontation against the Reapers.
That makes the Reapers in Mass Effect more like force of nature than an entity of cosmic horror - for that the suggestion of an alternative outcome by the whim of the cosmic entity must exist; that's why the good cosmic horror comes not just from the powerlessness in face of cosmic-scale entity but from the suggestion that that entity could possibly do different. That's why the vulgar misunderstanding of mental illness plays into some stories of cosmic horror - abandoning common sense and plunging oneself so deep into the incomprehensible to be damaged is desperate course of action because the possibility of an alternative outcome exists.
The way it worked out was probably the only way it would have every worked out.
EDIT ps. This is also the same reason why the Markers from Dead Space don't work as cosmic horror.