$U_\omega$ and $U_s = 2|s\rangle\langle s| - I$ are unitary

Let $f\colon\{0,\dots,N-1\}\to\{0,1\}$, let $U_\omega|x\rangle = (-1)^{f(x)}|x\rangle$ be the phase oracle and let $U_s = 2|s\rangle\langle s| - I$ be the Grover diffusion operator, where $|s\rangle = \frac{1}{\sqrt N}\sum_x|x\rangle$. Then both are unitary:

Both steps of a Grover iteration are therefore legitimate quantum operations, and the state of the algorithm stays normalized, so that the measurement probabilities of later milestones are probabilities.