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Long-duration $γ$-ray bursts (GRBs) accompany the collapse of massive stars and carry information about the central engine. However, no 3D models have been able to follow these jets from their birth by a black-hole (BH) to the photosphere. We present the first such 3D general-relativity magnetohydrodynamic simulations, which span over 6 orders of magnitude in space and time. The collapsing stellar envelope forms an accretion disk, which drags inwardly the magnetic flux that accumulates around the BH, becomes dynamically important and launches bipolar jets. The jets reach the photosphere at $\sim10^{12}$ cm with an opening angle $θ_j\sim6^\circ$ and a Lorentz factor $Γ_j\lesssim 30$, unbinding $\gtrsim90\%$ of the star. We find that (i) the disk-jet system spontaneously develops misalignment relative to the BH rotational axis. As a result, the jet wobbles with an angle $θ_t\sim12^\circ$, which can naturally explain quiescent times in GRB lightcurves. The effective opening angle for detection $θ_j+θ_t$ suggests that the intrinsic GRB rate is lower by an order of magnitude than standard estimates. This suggests that successful GRBs may be rarer than currently thought and emerge in only $\sim 0.1\%$ of supernovae Ib/c, implying that jets are either not launched or choked inside most supernova Ib/c progenitors. (ii) The magnetic energy in the jet decreases due to mixing with the star, resulting in jets with a hybrid composition of magnetic and thermal components at the photosphere, where $\sim 10\%$ of the gas maintains magnetization $σ\gtrsim 0.1$. This indicates that both a photospheric component and reconnection may play a role in the prompt emission.