  Signatures of strong-field quantum electrodynamics are determined for
collisions between round ultrarelativistic leptonic beams in the quantum limit
of beamstrahlung. In the low disruption regime, we derive the integrated
beamstrahlung photon spectrum that features a characteristic peak close to the
beam energy. The conditions to precisely observe this peak experimentally are
given regarding the beam parameters. Moreover, the effects of electron-positron
pair creation and beam disruption on the photon spectrum are discussed and
explored with 3-dimensional particle-in-cell QED simulations. The photon
spectrum is associated with the emission of ultrashort and highly collimated
gamma-ray beams with a peak spectral brightness exceeding $10^{30}\
\mathrm{photons}/(\mathrm{s}\ \mathrm{mm}^2\ \mathrm{mrad}^2\ 0.1\%
\mathrm{BW})$ at $100\ \mathrm{GeV}$-level photon energies (close to the beam
energy).
