Judging by when they made their actual Blades debut, either as a starter or a sub, League or Cup competition:
Looked some of these up on Wikipedia so I hope these figures are accurate
Including players currently out on loan but still contracted at SUFC.
Current 5 longest serving players (by debut):
1) Femi Seriki: Vs Newcastle, Premier League, May 2021 (late substitute)
2) RND: Vs Huddersfield, Championship, August 2021 (first appearance and first start)
3) Oliver Arblaster: Vs WBA, League Cup, August 2022 (it didn't say if he started or came of the bench), made his Championship debut from the bench a few weeks later against Hull in September
4) Adam Davies: Vs Coventry, Championship, October 2022 (initially signed in January 2022)
5) Andre Brooks: Vs Burnley, Championship, November 2022 (late substitute)