Context. Early theoretical works suggested that ultrahot Jupiters have inverted temperature-pressure (T-P) profiles in the presence of optical absorbers, such as TiO and VO. Recently, an inverted T-P profile of KELT-7b was detected, in agreement with the predictions. However, the diagnosis of T-P inversions has always been recognized to be a model-dependent process. Aims. We used the Characterising Exoplanet Satellite (CHEOPS), the Transiting Exoplanet Survey Satellite (TESS), and additional literature data to characterize the atmosphere of KELT-7b, rederive the T-P profile, provide a precise measurement of the albedo of KELT-7b, and search for a possible distortion in the precise CHEOPS transit light curve of the planet. Methods. We first jointly fitted the CHEOPS and TESS data and measured the occultation depths in these passbands. The CHEOPS transits were also fitted with a model including the gravity-darkening effect. Emission and absorption retrievals were performed to characterize the atmosphere of KELT-7b. The albedo of the planet was calculated in the CHEOPS and TESS passbands. Results. When adopting a thermochemical-equilibrium atmospheric composition, the emission retrievals return a non-inverted T-P profile, in contrast with previous results. When adopting a free-chemistry atmospheric parameterization, the emission retrievals return an inverted T-P profile with - likely unphysically - high concentrations of TiO and VO. The 3D general circulation model (GCM) supports a TiO-induced temperature inversion. We report for KELT-7b a very low geometric albedo of A(g) = 0.05 +/- 0.06, which is consistent with the heat distribution & varepsilon; being close to zero and also consistent with a 3D GCM simulation, using magnetic drag (tau(drag) = 10(4) s). Based on the CHEOPS photometry, we are unable to place any meaningful constraint on the sky-projected orbital obliquity. Conclusions. The choice of a free-chemistry approach or a thermochemical-equilibrium chemistry is the main factor determining the retrieval results. Free-chemistry retrievals generally yield better fits; however, assuming free chemistry risks adopting unphysical scenarios for ultrahot Jupiters, such as KELT-7b. We applied a coherent stellar variability treatment on TESS and CHEOPS observations, commensurate with the known stellar activity of the host star. Other observations of KELT-7b would also benefit from a coherent stellar variability treatment.