Proper conflict-free degree-choosability of graphs with maximum average degree less than $8/3$

A proper coloring $φ$ of a graph $G$ is called proper conflict-free if, for every non-isolated vertex $v$, some color appears exactly once in its open neighborhood $N_G(v)$. For a nonnegative integer $k$, a graph $G$ is proper conflict-free $(\mathrm{degree}+k)$-choosable if, for every list assignme