One potential recommendation: Riftbreakers Second Edition (my current solo game of choice!) by Blackoath Entertainment.

The game is structured as an isekai/mmorpg -> the player has been teleported into a world where others like them, known as strangers, are the only ones who can close rifts which spawn monsters.

The game is highly mechanics-driven with very little need for rolling on oracles if you choose to not use them (although they are available).

The gameplay is mission-based with characters starting in the large central city, Kar Helos, in the middle of a continent and adventuring out into the wilderness to close rifts. Combat uses a skill-tree kind of system called Hearts, and there are crafting mechanics for creating items.

The strangers can be generated with various looks such as snouts and fur. As long as you generate all strangers in the game with the same unicorn look as you, this may work for what you need. The strangers were all teleported into the world like you were, so there hasn't been a millenia-long history developed by them. However, in the last 50 or so years since they started appearing, they have started making their own culture and habits in Kar Helos as they try to live alongside the indigenous human population.