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 via black hole (BH) to the photosphere. We present the first such 3D general-relativity magnetohydrodynamic simulations, which span over six 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 ∼1012 cm with an opening angle θ j ∼ 6° and a Lorentz factor Γ j ≲ 30, unbinding ≳90% 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 ∼ 12°, 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 are rarer than currently thought and emerge in only ∼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 ∼10% of the gas maintains magnetization σ ≳ 0.1. This indicates that both a photospheric component and reconnection may play a role in the prompt emission.