It remains a major challenge to derive a theory of cloud-scale ($lesssim100$ 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-ALMA survey. We measure the spatially-resolved ($sim100$ 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 $Sigma_{rm H_2}geqslant8$M$_{odot}$pc$^{-2}$, the GMC lifetime correlates with time-scales for galactic dynamical processes, whereas at $Sigma_{rm H_2}leqslant8$M$_{odot}$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% 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% These results show that galactic star formation is governed by cloud-scale, environmentally-dependent, dynamical processes driving rapid evolutionary cycling. GMCs and HII regions are the fundamental units undergoing these lifecycles, with mean separations of 100-300 pc in star-forming discs. Future work should characterise the multi-scale physics and mass flows driving these lifecycles.
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