  Gravitational waves (GWs) provide a unique opportunity to test General
Relativity (GR) in the highly dynamical, strong-field regime. So far, the
majority of the tests of GR with GW signals have been carried out following
parametrized, theory-independent approaches. An alternative avenue consists in
developing inspiral-merger-ringdown (IMR) waveform models in specific beyond-GR
theories of gravity, by combining analytical and numerical-relativity results.
In this work, we provide the first example of a full IMR waveform model in a
beyond-GR theory, focusing on Einstein-scalar-Gauss-Bonnet (ESGB) gravity. This
theory has attracted particular attention due to its rich phenomenology for
binary black-hole (BH) mergers, thanks to the presence of non-trivial scalar
fields. Starting from the state-of-the art, effective-one-body (EOB) multipolar
waveform model for spin-precessing binary BHs SEOBNRv5PHM, we include
theory-specific corrections to the EOB Hamiltonian, the metric and scalar
energy fluxes, the GW modes, the quasi-normal-mode (QNM) spectrum and the mass
and spin of the remnant BH. We also propose a way to marginalize over the
uncertainty in the merger morphology with additional nuisance parameters.
Interestingly, we observe that changes in the frequency of the ringdown
waveform due to the final mass and spin corrections are significantly larger
than those due to ESGB corrections to the QNM spectrum. By performing Bayesian
parameter estimation for the GW events GW190412, GW190814 and GW230529_181500,
we place constraints on the fundamental coupling of the theory
($\sqrt{\alpha_{\mathrm{GB}}} \lesssim 0.31~\mathrm{km}$ at 90% confidence).
The bound could be improved by one order of magnitude by observing a single
"golden" binary system with next-generation ground-based GW detectors.
