Despite recent progress in the spectroscopic characterization of individual exoplanets, the atmospheres of key ultra-hot Jupiters (UHJs) still lack comprehensive investigations. These include WASP-178b, one of the most irradiated UHJs known to date. We observed the dayside emission signal of this planet with CRIRES$^+$ in the spectral K band. By applying the cross-correlation technique and a Bayesian retrieval framework to the high-resolution spectra, we identified the emission signature of 12CO (S/N\,=\,8.9) and H$_2$O (S/N\,=\,4.9), and a strong atmospheric thermal inversion. A joint retrieval with space-based secondary eclipse measurements from TESS and CHEOPS allowed us to refine our results on the thermal profile and thus to constrain the atmospheric chemistry, yielding a solar to super-solar metallicity ($1.4 and a solar C/O ratio ($0.6 We infer a significant excess of spectral line broadening and identify a slight Doppler-shift between the 12CO and H$_2$O signals. These findings provide strong evidence for a super-rotating atmospheric flow pattern and suggest the possible existence of chemical inhomogeneities across the planetary dayside hemisphere. In addition, the inclusion of photometric data in our retrieval allows us to account for stellar light reflected by the planetary atmosphere, resulting in an upper limit on the geometric albedo (0.23). The successful characterization of WASP-178b's atmosphere through a joint analysis of CRIRES$^+$, TESS, and CHEOPS observations highlights the potential of combined studies with space- and ground-based instruments and represents a promising avenue for advancing our understanding of exoplanet atmospheres.