This could well be a question for reading suggestion. Hope it's not too bad and thanks a lot.

So the question is as in the title. What are the relations between the notion of unipotent cuspidal representations of $G(\mathbb{F}_q)$, and that of cuspidal local systems as in generalized Springer theory, if any? For example, I notice that for classical groups of type $\mathbf{C}$, there exists a cuspidal local system for $\mathbf{C}_n$ iff there exists a unipotent cuspidal representations for $\mathbf{C}_{2n}$. Same for type $\mathbf{D}$. (For type $\mathbf{B}$, while there exist cuspidal local systems for $\mathrm{SO}_{n^2}$ and $\mathrm{SO}_{(n+1)^2}$, there exists a unipotent cuspidal representations for $SO_{n^2+(n+1)^2}$.)

This doesn't look like coincidence to me. Though by the time of the 1977 paper of Lusztig on representations of finite classical groups, he hasn't invented generalized Springer theory yet...