  Aims. Our goal is the characterization of the hot ejecta and shocked
interstellar medium (ISM) associated to the Vela supernova remnant (SNR), as
well as the relativistic electrons injected into the ambient medium by its
central pulsar. To achieve this, we analyze the X-ray data set of Vela acquired
by SRG/eROSITA during its first four all-sky surveys. Methods. Apart from
multi-band imaging, a quantitative view of the physical parameters affecting
the observed thermal and non-thermal emission is obtained by performing
spatially resolved X-ray spectroscopy of over 500 independent regions using
multi-component spectral models. Results. Imaging demonstrates that the X-ray
emission of the Vela SNR consists of at least three morphologically distinct
components, with shell-like structures dominating below 0.6 keV, radial
outward-directed features becoming apparent at medium energies, and the pulsar
wind nebula (PWN) dominating the hard emission above 1.4 keV. Our spectroscopy
reveals a highly structured distribution of X-ray absorption column densities,
which intriguingly appears anticorrelated with optical extinction measurements.
We find evidence for multiple ejecta clumps inside and outside the shell,
within which we find a strongly supersolar concentration of neon and magnesium
relative to oxygen. This includes the bright shrapnel D, in which we separate
shocked ISM in the soft bow-shock from a hot, ejecta-rich clump at its apex,
based on the new data. Finally, we find an extremely extended, smoothly
decreasing distribution of synchrotron emission from the PWN, which extends up
to 14 pc from the pulsar, with a total X-ray luminosity of $1.5\times10^{-3}$
of the pulsar's spin-down power. The extended emission likely traces a
relativistic electron population in an ISM-level magnetic field, which requires
the existence of a TeV counterpart powered by inverse Compton radiation.
