  We present a tree tensor-network impurity solver suited for general
multiorbital systems. The network is constructed to efficiently capture the
entanglement structure and symmetry of an impurity problem. The solver works
directly on the real-time/frequency axis and generates spectral functions with
energy-independent resolution of the order of one percent of the correlated
bandwidth. Combined with an optimized representation of the impurity bath, it
efficiently solves self-consistent dynamical mean-field equations and
calculates various dynamical correlation functions for systems with
off-diagonal Green's functions. For the archetypal correlated Hund's metal
Sr$_2$RuO$_4$, we show that both the low-energy quasiparticle spectra related
to the van Hove singularity and the high-energy atomic multiplet excitations
can be faithfully resolved. In particular, we show that while the spin-orbit
coupling has only minor effects on the orbital-diagonal one-particle spectral
functions, it has a more profound impact on the low-energy spin and orbital
response functions.
