Sheffield were promoted out of the Northern Counties East League Premier Division in 2006/07 (Hallam finished 14th). And, I believe, since then, have played at a higher Step than Hallam. This season, 2024/25, they have by-passed each other. Hallam have been promoted, and Sheffield have been relegated.
From 1994/95 until 2005/06 both Hallam and Sheffield were in the same division.
From 1991/92 until 1993/94, Sheffield were in a higher division than Hallam.
From 1989/90 until 1990/91 both Hallam and Sheffield were in the same division.
In 1988/89, Hallam finished 12th in the Northern Counties East Premier. Sheffield finished 1st in the, lower, Northern Counties East Division One. To answer your question, 1988/89 was the last season Hallam competed in a higher league than Sheffield.
During the entire period I explain, Hallam have been a club anchored at their historical home ground, building a sustainable model based around Club House takings and increasing gate and sponsorship revenue.
Over the same period, Sheffield FC have had more artists impressions of "new grounds" than they have fans attending an average home match. Currently, they have had to remove a sign at their latest "new ground" because the sign itself did not have fucking planning permission. Their main business model remains - send money now, did we mention we're the oldest club in the world....