Context. Multi-planet systems are important sources of information regarding the evolution of planets. However, the long-period planets in these systems often escape detection. These objects in particular may retain more of their primordial characteristics compared to close-in counterparts because of their increased distance from the host star. HD 22946 is a bright (G = 8.13 mag) late F-type star around which three transiting planets were identified via Transiting Exoplanet Survey Satellite (TESS) photometry, but the true orbital period of the outermost planet d was unknown until now. Aims. We aim to use the Characterising Exoplanet Satellite (CHEOPS) space telescope to uncover the true orbital period of HD 22946d and to refine the orbital and planetary properties of the system, especially the radii of the planets. Methods. We used the available TESS photometry of HD 22946 and observed several transits of the planets b, c, and d using CHEOPS. We identified two transits of planet d in the TESS photometry, calculated the most probable period aliases based on these data, and then scheduled CHEOPS observations. The photometric data were supplemented with ESPRESSO (Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observations) radial velocity data. Finally, a combined model was fitted to the entire dataset in order to obtain final planetary and system parameters. Results. Based on the combined TESS and CHEOPS observations, we successfully determined the true orbital period of the planet d to be 47.42489 +/- 0.00011 days, and derived precise radii of the planets in the system, namely 1.362 +/- 0.040 R-circle plus, 2.328 +/- 0.039 R-?, and 2.607 +/- 0.060 R-circle plus for planets b, c, and d, respectively. Due to the low number of radial velocities, we were only able to determine 3s upper limits for these respective planet masses, which are 13.71 M-circle plus 9.72 M-?, and 26.57 M-circle plus. We estimated that another 48 ESPRESSO radial velocities are needed to measure the predicted masses of all planets in HD 22946. We also derived stellar parameters for the host star. Conclusions. Planet c around HD 22946 appears to be a promising target for future atmospheric characterisation via transmission spectroscopy. We can also conclude that planet d, as a warm sub-Neptune, is very interesting because there are only a few similar confirmed exoplanets to date. Such objects are worth investigating in the near future, for example in terms of their composition and internal structure.