Context. Ultra-hot Jupiters (UHJs) are gas giant exoplanets that are strongly irradiated by their star, setting intense molecular dissociation that leads to atmospheric chemistry dominated by ions and atoms. These conditions inhibit day-to-night heat redistribution, which results in high temperature contrasts. Phase-curve observations over several passbands offer insights on the thermal structure and properties of these extreme atmospheres. Aims. We aim to perform a joint analysis of multiple observations of WASP-18 b from the visible to the mid-infrared, using data from CHEOPS, TESS, and Spitzer. Our purpose is to characterise the planetary atmosphere with a consistent view over the large wavelength range covered, including JWST data. Methods. We implemented a model for the planetary signal including transits, occultations, phase signal, ellipsoidal variations, Doppler boosting, and light travel time. We performed a joint fit of more than 250 eclipse events and derived the atmospheric properties using general circulation models (GCMs) and retrieval analyses. Results. We obtained new ephemerides with unprecedented precisions of 1 second and 1.4 millisecond on the time of inferior conjunction and orbital period, respectively. We computed a planetary radius of R p = 1.1926 ± 0.0077 R J with a precision of 0.65% (or 550 km). Based on a timing inconsistency with JWST, we discuss and confirm the orbital eccentricity (e = 0.00852 ± 0.00091). We also constrain the argument of periastron to ω = 261.9‑1.4 +1.3 deg. We show that the large dayside emission implies the presence of magnetic drag and super-solar metallicity. We find a steep thermally inverted gradient in the planetary atmosphere, which is common for UHJs. We detected the presence of strong CO emission lines at 4.5 μm from an excess of dayside brightness in the Spitzer/IRAC/Channel 2 passband. Using these models to constrain the reflected contribution in the CHEOPS passband, we derived an extremely low geometric albedo of Ag CHEOPS = 0.027 ± 0.011. Conclusions. The orbital eccentricity remains a potential challenge for planetary dynamics that might require further study given the short-period massive planet and despite the young age of the system. The characterisation of the atmosphere of WASP-18 b reveals the necessity to account for magnetic friction and super-solar metallicity to explain the full picture of the dayside emission. We find the planetary dayside to be extremely unreflective; however, when juxtaposing TESS and CHEOPS data, we get hints of increased scattering efficiency in the visible, likely due to Rayleigh scattering.