Observational campaigns hunting the elusive reservoirs of cold gas in the host galaxies of quasars at the epoch of reionization (EoR) are crucial for studying the formation and evolution of the first massive systems at early epochs. We present new Northern Extended Millimeter Array (NOEMA) observations tracing CO(6-5) and CO(7-6) emission lines as well as the underlying continuum in five of the eight quasars at redshift z > 7 known to date, thus completing the survey of the cold molecular gas reservoir in the host galaxies of the first quasars. Combining NOEMA observations with archival Atacama Large Millimeter/submillimeter Array (ALMA) data, we modeled the far-infrared spectral energy distribution with a modified blackbody function to measure dust properties and star formation rates. We used CO and [CII] lines to derive molecular gas masses, which we compared with results from semi-analytic models and observations of galaxies at different epochs. No statistically significant detection of CO emission lines was reported for the five quasars in this sample, resulting in a relatively low amount of cold molecular gas in the host when compared with galaxies at later epochs. Nonetheless, gas-to-dust ratios are consistent with the local value, suggesting that the scaling relation between dust and cold gas holds up to z > 7. Quasars at the EoR show star formation efficiencies that are among the highest observed so far and comparable with those observed in luminous quasars at Cosmic Noon and those predicted for the brightest (Lbol > 3 x 1046 erg s-1) quasar objects drawn from the semi-analytic model GAEA. Quasar host galaxies at the EoR are undergoing an intense phase of star formation, which suggests a strong coupling between the luminous phase of the quasar and the rapid growth of the host.