It remains a major challenge to derive a theory of cloud-scale (less than or similar to 100 pc) star formation and feedback, describing how galaxies convert gas into stars as a function of the galactic environment. Progress has been hampered by a lack of robust empirical constraints on the giant molecular cloud (GMC) lifecycle. We address this problem by systematically applying a new statistical method for measuring the evolutionary timeline of the GMC lifecycle, star formation, and feedback to a sample of nine nearby disc galaxies, observed as part of the PHANGS-AINIA survey. We measure the spatially resolved (similar to 100 pc) CO-to-H alpha flux ratio and find a universal de-correlation between molecular gas and young stars on GMC scales, allowing us to quantify the underlying evolutionary timeline. GMC lifetimes are short, typically 10-30 Myr, and exhibit environmental variation, between and within galaxies. At kpc-scale molecular gas surface densities Sigma(H2) >= 8 M-circle dot pc(-2), the GMC lifetime correlates with timescales for galactic dynamical processes, whereas at Sigma(H2) >= 8 M-circle dot pc(-2) GMCs decouple from galactic dynamics and live for an internal dynamical time-scale. After a long inert phase without massive star formation traced by H alpha (75-90 per cent of the cloud lifetime), GMCs disperse within just 1-5 Myr once massive stars emerge. The dispersal is most likely due to early stellar feedback, causing GMCs to achieve integrated star formation efficiencies of 4-10 per cent. These results show that galactic star formation is governed by cloud-scale, environmentally dependent, dynamical processes driving rapid evolutionary cycling. GMCs and H II regions are the fundamental units undergoing these lifecycles, with mean separations of 100-300 pc in star-forming discs. Future work should characterize the multiscale physics and mass flows driving these lifecycles.