  Eccentric mergers are a signature of the dynamical formation channel of
binary black holes (BBHs) in dense stellar environments and hierarchical triple
systems. Here, we investigate the formation of eccentric mergers via
binary-single interactions by means of $2.5\times10^{5}$ direct
$\textit{N}$-body simulations. Our simulations include post-Newtonian terms up
to the 2.5th order and model the typical environment of young (YSCs), globular
(GCs), and nuclear star clusters (NSCs). Around $0.6\%$ ($1\%$) of our mergers
in NSCs (GCs) have an eccentricity ${>0.1}$ when the emitted gravitational wave
frequency is 10 Hz in the source frame, while in YSCs this fraction rises to
$1.6\%$. Approximately $\sim63\%$ of these mergers are produced by chaotic,
resonant interactions where temporary binaries are continuously formed and
destroyed, while $\sim31\%$ arise from an almost direct collision of two black
holes (BHs). Lastly, $\sim 6\%$ of these eccentric mergers occur in temporary
hierarchical triples. We find that binaries undergoing a flyby generally
develop smaller tilt angles with respect to exchanges. This result challenges
the idea that perfectly isotropic spin orientations are produced by dynamics.
The environment dramatically affects BH retention: $0\%$, $3.1\%$, and $19.9\%$
of all the remnant BHs remain in YSCs, GCs, and NSCs, respectively. The
fraction of massive BHs also depends on the host cluster properties, with
pair-instability ($60\leq\,$M$_{\rm BH}$/M$_{\odot}\leq$100) and
intermediate-mass (M$_{\rm BH}\geq$100$\,$M$_{\odot}$) BHs accounting for
approximately $\sim44\%$ and $1.6\%$ of the mergers in YSCs, $\sim33\%$ and
$0.7\%$ in GCs, and $\sim28\%$ and $0.4\%$ in NSCs, respectively.
