  We investigate the structural, electronic, transport, and thermoelectric
properties of LaNiO$_3$/SrTiO$_3(001)$ superlattices containing either
exclusively $n$- or $p$-type interfaces or coupled interfaces of opposite
polarity by using density functional theory calculations with an on-site
Coulomb repulsion term. The results show that significant octahedral tilts are
induced in the SrTiO$_3$ part of the superlattice. Moreover, the La-Sr
distances and Ni-O out-of-plane bond lengths at the interfaces exhibit a
distinct variation by about $7\,\%$ with the sign of the electrostatic doping.
In contrast to the much studied LaAlO$_3$/SrTiO$_3$ system, the charge mismatch
at the interfaces is exclusively accommodated within the LaNiO$_3$ layers,
whereas the interface polarity leads to a band offset and to the formation of
an electric field within the coupled superlattice. Features of the electronic
structure indicate an orbital-selective quantization of quantum well states.
The potential- and confinement-induced multiband splitting results in complex
cylindrical Fermi surfaces with a tendency towards nesting that depends on the
interface polarity. The analysis of the thermoelectric response reveals a
particularly large positive Seebeck coefficient ($135~\mu$V/K) and a high
figure of merit ($0.35$) for room-temperature cross-plane transport in the
$p$-type superlattice that is attributed to the participation of the SrTiO$_3$
valence band. Superlattices with either $n$- or $p$-type interfaces show
cross-plane Seebeck coefficients of opposite sign and thus emerge as a platform
to construct an oxide-based thermoelectric generator with structurally and
electronically compatible $n$- and $p$-type oxide thermoelectrics.
