  The production of ground-state and excited bottomonia in ultrarelativistic
heavy-ion collisions is investigated within a kinetic-rate equation approach
including regeneration. We augment our previous calculations by an improved
treatment of medium effects, with temperature-dependent binding energies and
pertinent reaction rates, $B$-meson resonance states in the equilibrium limit
near the hadronization temperature, and a lattice-QCD based equation of state
for the bulk medium. In addition to the centrality dependence of the
bottomonium yields we compute their transverse-momentum ($p_T$) spectra and
elliptic flow with momentum-dependent reaction rates and a regeneration
component based on $b$-quark spectra from a nonperturbative transport model of
heavy-quark diffusion. The latter has noticeable consequences for the shape of
the bottomonium $p_T$ spectra. We quantify how uncertainties in the various
modeling components affect the predictions for observables. Based on this we
argue that the $\Upsilon(1S)$ suppression is a promising observable for mapping
out the in-medium properties of the QCD force, while $\Upsilon(2S)$ production
can help to quantify the role of regeneration from partially thermalized $b$
quarks.
