  We introduce bivariate versions of the continuous q-Hermite polynomials. We
obtain algebraic properties for them (generating function, explicit expressions
in terms of the univariate ones, backward difference equations and recurrence
relations) and analytic properties (determining the orthogonality measure). We
find a direct link between bivariate continuous q-Hermite polynomials and the
star product method of [Kolb and Yakimov, Adv. Math. 2020] for quantum
symmetric pairs to establish deformed quantum Serre relations for quasi-split
quantum symmetric pairs of Kac-Moody type. We prove that these defining
relations are obtained from the usual quantum Serre relations by replacing all
monomials by multivariate orthogonal polynomials.
