  The main result of the present paper concerns finiteness properties of Floer
theoretic invariants on affine log Calabi-Yau varieties $X$. Namely, we show
that:
  (a) the degree zero symplectic cohomology $SH^0(X)$ is finitely generated and
is a filtered deformation of a certain algebra defined combinatorially in terms
of a compactifying divisor $\mathbf{D}.$ (b) For any Lagrangian branes $L_0,
L_1$, the wrapped Floer groups $WF^*(L_0,L_1)$ are finitely generated modules
over $SH^0(X).$
  We then describe applications of this result to mirror symmetry, the first of
which is an ``automatic generation" criterion for the wrapped Fukaya category
$\mathcal{W}(X)$. We also show that, in the case where $X$ is maximally
degenerate and admits a ``homological section", $\mathcal{W}(X)$ gives a
categorical crepant resolution of the potentially singular variety
$\operatorname{Spec}(SH^0(X))$. This provides a link between the intrinsic
mirror symmetry program of Gross and Siebert and the categorical birational
geometry program initiated by Bondal-Orlov and Kuznetsov.
