We image the rupture process of the 2021 Mw 7.4 Maduo, Tibet earthquake using slowness-enhanced back-projection and joint finite fault inversion, which combines teleseismic broadband body waves, long-period (166-333 s) seismic waves, and 3D ground displacements from radar satellites. The results reveal a left-lateral strike-slip rupture, propagating bilaterally on a 160-km-long north-dipping sub-vertical fault system that bifurcates near its east end. About 80% of the total seismic moment occurs on the asperities shallower than 10 km, with a peak slip of 5.7 m. To simultaneously match the observed long-period seismic waves and static displacements, notable deep slip is required, despite a tradeoff with the rigidity of the shallow crust. This coseismic deep slip within the ductile middle crust could result from strain localization and dynamic weakening. Local crustal structure and synthetic long-period Earth response for Tibet earthquakes thus deserve further investigation. The WNW branch ruptures ~75 km at ~2.7 km/s, while the ESE branch ruptures ~85 km at ~3 km/s, though super-shear rupture propagation possibly occurs during the ESE propagation from 12 s to 20 s. Synthetic back-projection tests confirm overall sub-shear rupture speeds and reveal a previously undocumented limitation caused by the signal interference between two bilateral branches. The stress analysis on the forks of the fault demonstrates that the pre-compression inclination, rupture speed, and branching angle could explain the branching behavior on the eastern fork.