Do any books or articles develop basic Euclidean geometry from the perspective of "inner product affine spaces"?
Perhaps you might like Audin's Geometry.
From the intro:
The first idea is to give a rigorous exposition, based on the definition of an affine space via linear algebra, but not hesitating to be elementary and down-to-earth. I have tried both to explain that linear algebra is useful for elementary geometry (after all, this is where it comes from) and to show “genuine” geometry: triangles, spheres, polyhedra, angles at the circumference, inversions, parabolas...
Chapter 1 is titled Affine Geometry, the next three chapters are about Euclidean geometry (generalities, in the plane, and in space), followed by projective geometry and then a few chapters on classical topics (conic sections, curves, surfaces).