Einstein realized a 4D field (length:width:depth:time) produces a field which, when distorted by mass, describes gravity.
Later, the Kaluza-Klein theory came abou by extending General Relativity to 5 dimensions…describing Gravity AND electromagnetizm.
Question is…what is found when you use the rules and formulation of GR/KK and restrict the field to only 3 or even 2 dimensions?
I assume that by 3 or 2 dimensions, you mean 2+1 or 1+1, with one timelike dimension and the rest spatial, as that’s important in order to get anything interesting out of GR.
The short answer is that in either case, you get something which could be generously described as “gravity”, but that the “gravity” you get is extremely boring. In 2+1 dimensional gravity, you get curvature only where the masses are, and flat space everywhere you have vacuum. There is no distance dependence of gravity and nothing that behaves like a force, and no closed orbits. The geometry outside of a mass is conical, meaning that two trajectories which start off parallel will meet shortly after passing on opposite sides of a mass, but neither will show any evidence of curvature. In 1+1 dimensional gravity, I don’t think you get any effects at all unless you also posit that mass isn’t conserved.
Oh, and I should also mention that, while 4+1 Kaluza-Klein is a neat trick, it’s not consistent with QED, and is thus not taken seriously as a realistic theory of electromagnetism nowadays. On the other hand, you can consider the String Model as a generalization of the same idea, and nobody has yet managed to disprove that one.