  We present the first systematic search for exotic compact mergers in Advanced
LIGO and Virgo events. We compare the short gravitational-wave signals
GW190521, GW190426$\_$190642, GW200220$\_$061928 and the trigger
200114$\_$020818 (or S200114f) to a new catalogue of 759 numerical simulations
of head-on mergers of horizonless exotic compact objects known as Proca stars,
interpreted as self-gravitating lumps of (fuzzy) dark matter sourced by an
ultralight (vector) bosonic particle. The Proca-star merger hypothesis is
strongly rejected with respect to the black hole merger one by GW190426, weakly
rejected by GW200220 and weakly favoured by GW190521 and S200114f. GW190521 and
GW200220 yield highly consistent boson masses of $\mu_{\rm B} =
8.69^{+0.61}_{-0.75}\times10^{-13}$ eV and $\mu_{\rm B} =
9.13^{+1.18}_{-1.30}\times10^{-13}$ eV at the $90\%$ credible level. We conduct
a preliminary population study of the compact binaries behind these events.
Excluding (including) S200114f as a real event, and ignoring boson-mass
consistencies across events, we estimate a fraction of Proca-star mergers of
$\zeta = 0.27^{+0.43}_{-0.25} \ (0.39^{+0.38}_{-0.33})$. We discuss the impact
of boson-mass consistency across events in such estimates. Our results maintain
GW190521 as a Proca-star merger candidate and pave the way towards population
studies considering exotic compact objects.
