  Circumgalactic Lyman-alpha (Ly$\alpha$) nebulae are gaseous halos around
galaxies exhibiting luminous extended Ly$\alpha$ emission. This work
investigates Ly$\alpha$ nebulae from deep imaging of $\sim12~\mathrm{deg}^2$
sky, targeted by the MAMMOTH-Subaru survey. Utilizing the wide-field capability
of Hyper Suprime-Cam (HSC), we present one of the largest blind Ly$\alpha$
nebula selections, including QSO nebulae, Ly$\alpha$ blobs, and radio galaxy
nebulae down to typical $2\sigma$ Ly$\alpha$ surface brightness of
$(5-10)\times10^{-18}\mathrm{~erg~s^{-1}~cm^{-2}~arcsec^{-2}}$. The sample
contains 117 nebulae with Ly$\alpha$ sizes of 40 - 400 kpc, and the most
gigantic one spans about 365 kpc, referred to as the Ivory Nebula. Combining
with multiwavelength data, we investigate diverse nebula populations and
associated galaxies. We find a small fraction of Ly$\alpha$ nebulae have QSOs
($\sim7\%$), luminous infrared galaxies ($\sim1\%$), and radio galaxies ($\sim
2\%$). Remarkably, among the 28 enormous Ly$\alpha$ nebulae (ELANe) exceeding
100 kpc, about $80\%$ are associated with UV-faint galaxies ($M_\mathrm{UV} >
-22$), 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 SED 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$\alpha$ nebula capture massive galaxies at different evolutionary stages
undergoing violent assembling. Ly$\alpha$ nebulae provide critical insights
into the formation and evolution of today's massive cluster galaxies at cosmic
noon.
