Investigate making `prune_dead_locals` more aggressive by tracing liveness from variables in `SideEffects`

This serves as a tracking issue to follow up conversation from another PR: https://github.com/pytorch/pytorch/pull/136891#discussion_r1783356678.

cc @ezyang @chauhang @penguinwu @voznesenskym @EikanWang @jgong5 @Guobing-Chen @XiaobingSuper @zhuhaozhe @blzheng @wenzhe-nrv @jiayisunx @chenyang78 @kadeng @amjames @rec