  Generation of highly-polarized high-energy brilliant $\gamma$-rays via
laser-plasma interaction has been investigated in the quantum
radiation-reaction regime. We employ a quantum-electrodynamics particle-in-cell
code to describe spin-resolved electron dynamics semiclassically and photon
emission and polarization quantum mechanically in the local constant field
approximation. As an ultrastrong linearly-polarized (LP) laser pulse irradiates
on a near-critical-density (NCD) plasma followed by an ultrathin planar
aluminum target, the electrons in NCD plasma are first accelerated by the
driving laser to ultrarelativistic energies, and then head-on collide with
reflected laser pulse by the aluminum target, emitting brilliant LP
$\gamma$-rays due to nonlinear Compton scattering with an average polarization
of about 70\% and energy up to hundreds of MeV. By comparison, as a conical
gold target filled with NCD plasma is employed, the linear polarization degree,
collimation and brilliance of emitted $\gamma$-ray beam are all significantly
improved due to the enhanced strong laser-driven quasi-static magnetic field in
plasmas. Such $\gamma$-rays can be produced with currently achievable laser
facilities and find various applications in high-energy physics and
astrophysics.
