  We systematically study the field equations of $f(\mathbb Q)$ gravity for
spherically symmetric and stationary metric-affine spacetimes. Such spacetimes
are described by a metric as well as a flat and torsionless affine connection.
In the Symmetric Teleparallel Equivalent of GR (STEGR), the connection is pure
gauge and hence unphysical. However, in the non-linear extension $f(\Q)$, it is
promoted to a dynamical field which changes the physics. Starting from a
general metric-affine geometry, we construct the most general static and
spherically symmetric forms of the metric and the affine connection. We then
use these symmetry reduced geometric objects to prove that the field equations
of $f(\Q)$ gravity admit GR solutions as well as beyond-GR solutions, contrary
to what has been claimed in the literature. We formulate precise criteria,
under which conditions it is possible to obtain GR solutions and under which
conditions it is possible to obtain beyond-GR solutions. We subsequently
construct several perturbative corrections to the Schwarzschild solution for
different choices of $f(\Q)$, which in particular include a hair stemming from
the now dynamical affine connection. We also present an exact beyond-GR vacuum
solution. Lastly, we apply this method of constructing spherically symmetric
and stationary solutions to $f(\T)$ gravity, which reproduces similar solutions
but without a dynamical connection.
