  We present a systematic analysis of the X-ray emission of a sample of 17
optically selected, X-ray-detected tidal disruption events (TDEs) discovered
between 2014 and 2021. The X-ray light curves show a diverse range of temporal
behaviors, with most sources not following the expected power-law decline. The
X-ray spectra are mostly extremely soft and consistent with thermal emission
from the inner region of an accretion disk that cools as the accretion rate
decreases. Three sources show the formation of a hard X-ray corona around 200
days after the UV/optical peak. The shape of the spectral energy distribution,
traced by the ratio ($L_{\rm BB}/L_{\rm X}$) between the UV/optical and X-ray
luminosities, shows a wide range $L_{\rm BB}/L_{\rm X} \in (0.5, 3000)$ at
early-times, and converges to disk-like values $L_{\rm BB}/L_{\rm X} \in (0.5,
10)$ at late-times. The evolution of the derived physical parameters favors a
decrease in the optical depth of a reprocessing layer instead of delayed disk
formation to explain the late-time X-ray brightening found in several sources.
We estimate the fraction of optically discovered TDEs with $L_{\rm X}\geq
10^{42}$ erg s$^{-1}$ to be at least $40\%$, and find that the X-ray loudness
is independent of black hole mass. We combine our sample with those from X-ray
surveys to construct an X-ray luminosity function, best fitted by a broken
power-law with a brake at $\sim 10^{44}$ erg s$^{-1}$. We show that there is no
dichotomy between optically and X-ray selected TDEs; instead, there is a
continuum of early time $L_{\rm BB}/L_{\rm X}$, at least as wide as $L_{\rm
BB}/L_{\rm X} \in (0.1, 3000)$, with optical/X-ray surveys selecting
preferentially, but not exclusively, from the higher/lower end of the
distribution. Our findings are consistent with an orientation-dependent and
time-evolving reprocessing layer, and support viewing-angle unification models.

High Energy Astrophysical Phenomena;Astrophysics of Galaxies