  We exhibit examples of actions of countable discrete groups on both simple
and non-simple nuclear stably finite C*-algebras that are tracially amenable
but not amenable. We moreover obtain that, under the additional assumption of
strict comparison, amenability is equivalent to tracial amenability plus the
equivariant analogue of Matui--Sato's property (SI). By virtue of this
equivalence, our construction yields the first known examples of actions on
classifiable C*-algebras that do not have equivariant property (SI). We
moreover show that such actions can be chosen to absorb the trivial action on
the universal UHF algebra, thus showing that equivariant
$\mathcal{Z}$-stability does not in general imply equivariant property (SI).
