Circumgalactic Ly{alpha} nebulae are gaseous halos around galaxies exhibiting luminous extended Ly{alpha} emission. This work investigates Ly{alpha} nebulae from deep imaging of ~12 deg2 sky, targeted by the MAMMOTH-Subaru survey. Utilizing the wide-field capability of Hyper Suprime-Cam, we present one of the largest blind Ly{alpha} nebula selections, including QSO nebulae, Ly{alpha} blobs, and radio galaxy nebulae down to the typical 2{sigma} Ly{alpha} surface brightness of (5-10)x10^-18^erg/s/cm^2^/arcsec^2^. The sample contains 117 nebulae with Ly{alpha} sizes of 40-400kpc, and the most gigantic one spans about 365kpc, and is referred to as the Ivory Nebula. Combining multiwavelength data, we investigate diverse nebula populations and associated galaxies. We find a small fraction of Ly{alpha} nebulae have QSOs (~7%), luminous infrared galaxies (LIRGs; ~1%), and radio galaxies (~2%). Remarkably, among the 28 enormous Ly{alpha} nebulae (ELANe) exceeding 100kpc, about 80% are associated with UV-faint galaxies (M_UV_>-22), and are categorized as Type II ELANe. We underscore that Type II ELANe constitute the majority but remain largely hidden in current galaxy and QSO surveys. Dusty starburst and obscured AGN activity are proposed to explain the nature of Type II ELANe. The spectral energy distribution of stacking all Ly{alpha} nebulae also reveals signs of massive dusty star-forming galaxies with obscured AGNs. We propose a model to explain the dusty nature where the diverse populations of Ly{alpha} nebulae capture massive galaxies at different evolutionary stages undergoing violent assembly. Ly{alpha} nebulae provide critical insights into the formation and evolution of today's massive cluster galaxies at cosmic noon.