= Solution
A static worldline has <four-velocity>
$$
u^\mu=(f^{-1/2},0,0,0).
$$
Its <four-acceleration> is $a^\mu=u^\nu\nabla_\nu u^\mu$. The only nonzero component is
$$
a^r=\Gamma^r_{tt}(u^t)^2=\frac{M}{r^2}.
$$
Taking its norm with $g_{rr}=f^{-1}$ gives the <proper acceleration of a static Schwarzschild observer>
$$
\boxed{
|a|=\sqrt{a_\mu a^\mu}
=\frac{M}{r_{\rm st}^2\sqrt{1-2M/r_{\rm st}}}
}.
$$
It points radially outward, because that is the acceleration needed to prevent the station from falling. As $r_{\rm st}\to\infty$ the square-root factor tends to one, and $|a|\sim M/r_{\rm st}^2$, the <Newtonian gravitational field> in units $G=1$.
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