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Recent surveys have shown that z ≳ 2 quasars are surrounded by hydrogen Lyman- α (Ly α ) glows with diverse emission levels and extents. These characteristics seem to depend on the activity of embedded quasars, on the number of active galactic nucleus (AGN) photons that are able to reach the halo gas or circumgalactic medium (CGM), and on the physical properties of the CGM. In this framework, we present VLT/MUSE snapshot observations (45 minutes/source) of 59 z ∼ 3 quasars extending the long-term QSO MUSEUM campaign to the fainter SDSS sources. The whole survey is homogeneously reduced and analyzed here and now targets 120 quasars with a median redshift z = 3.13 and bolometric luminosities, black hole masses, and Eddington ratios in the ranges 45.1 < log( L bol /[erg s −1 ]) < 48.7, 7.9 < log( M BH /[M ⊙ ]) < 10.3, and 0.01 < λ Edd < 1.8. We detected extended Ly α emission in 110 of the 120 systems, with all the nondetections in the newly added fainter sample. The surface brightness of the CGM Ly α emission (SB Lyα ) increases with quasar luminosity. Stacking of the nondetections unveiled emission just below our individual field detection limit. Moreover, the Ly α line width increases in the central regions (projected radius R < 40 kpc or ∼40% R vir ) of the CGM around quasars with stronger radiation. The variation in surface brightness and the velocity dispersion as a function of quasar luminosity indicate that we witness the instantaneous AGN feedback in action on CGM scales. Assuming that all targeted quasars sit in halos of M DM ∼ 10 12.5 M ⊙ independent of luminosity, as suggested by clustering studies, we explain the trend in SB Lyα naturally by a larger fraction of cool gas mass that is illuminated, which implies that brighter quasars have larger ionization cone opening angles. Similarly, brighter AGN seem to perturb the cool ( T ∼ 10 4 K) gas more strongly. We show that QSO MUSEUM starts to have enough statistics to study this instantaneous AGN feedback while controlling for black hole properties (e.g., mass), which will be key to constraining AGN models.