  In heavy-ion collision experiments, the global collectivity of final-state
particles can be quantified by anisotropic flow coefficients ($v_n$). The
first-order flow coefficient, also referred to as the directed flow ($v_{1}$),
describes the collective sideward motion of produced particles and nuclear
fragments in heavy-ion collisions. It carries information on the very early
stage of the collision, especially at large pseudorapidity ($\eta$), where it
is believed to be generated during the nuclear passage time. Directed flow
therefore probes the onset of bulk collective dynamics during thermalization,
providing valuable experimental guidance to models of the pre-equilibrium
stage. In 2018, the Event Plane Detector (EPD) was installed in STAR and used
for the Beam Energy Scan phase-II (BES-II) data taking. The combination of EPD
($2.1 <|\eta|< 5.1$) and high-statistics BES-II data enables us to extend the
$v_{1}$ measurement to the forward and backward $\eta$ regions. In this paper,
we present the measurement of $v_{1}$ over a wide $\eta$ range in Au+Au
collisions at $\sqrt{s_{NN}}=$ 19.6 and 27 GeV using the STAR EPD. The results
of the analysis at $\sqrt{s_{NN}}=$19.6 GeV exhibit excellent consistency with
the previous PHOBOS measurement, while elevating the precision of the overall
measurement. The increased precision of the measurement also revealed finer
structures in heavy-ion collisions, including a potential observation of the
first-order event-plane decorrelation. Multiple physics models were compared to
the experimental results. Only a transport model and a three-fluid hybrid model
can reproduce a sizable $v_{1}$ at large $\eta$ as was observed experimentally.
The model comparison also indicates $v_{1}$ at large $\eta$ might be sensitive
to the QGP phase transition.
