  We use resonant elastic and inelastic X-ray scattering at the Ir-$L_3$ edge
to study the doping-dependent magnetic order, magnetic excitations and
spin-orbit excitons in the electron-doped bilayer iridate
(Sr$_{1-x}$La$_{x}$)$_3$Ir$_2$O$_7$ ($0 \leq x \leq 0.065$). With increasing
doping $x$, the three-dimensional long range antiferromagnetic order is
gradually suppressed and evolves into a three-dimensional short range order
from $x = 0$ to $0.05$, followed by a transition to two-dimensional short range
order between $x = 0.05$ and $0.065$. Following the evolution of the
antiferromagnetic order, the magnetic excitations undergo damping, anisotropic
softening and gap collapse, accompanied by weakly doping-dependent spin-orbit
excitons. Therefore, we conclude that electron doping suppresses the magnetic
anisotropy and interlayer couplings and drives
(Sr$_{1-x}$La$_x$)$_3$Ir$_2$O$_7$ into a correlated metallic state hosting
two-dimensional short range antiferromagnetic order and strong
antiferromagnetic fluctuations of $J_{\text{eff}} = \frac{1}{2}$ moments, with
the magnon gap strongly suppressed.
