  Relaxing the Bondi gauge, the solution space of three-dimensional gravity in
the metric formulation has been shown to contain an additional free function
that promotes the boundary metric to a Lorentz or Carroll frame, in
asymptotically AdS or flat spacetimes. We pursue this analysis and show that
the solution space also admits a finite symplectic structure, obtained taking
advantage of the built-in ambiguities. The smoothness of the flat limit of the
AdS symplectic structure selects a prescription in which the holographic
anomaly appears in the boundary Lorentz symmetry, that rotates the frame. This
anomaly turns out to be cohomologically equivalent to the standard holographic
Weyl anomaly and survives in the flat limit, thus predicting the existence of
quantum anomalies in conformal Carrollian field theories. We also revisit these
results in the Chern--Simons formulation, where the prescription for the
symplectic structure admitting a smooth flat limit follows from the variational
principle, and we compute the charge algebra in the boundary conformal gauge.
