In 那个是我工作上的东西, what is the difference between 工作上 and 工作?
上 here means about（相关）.

Try to understand it like this: 那个是我工作相关的东西

If you omit 上, it'd be understand as the item used for work rather than about.

那个是我工作的东西 sounds a bit like 那个是我工作用的东西.

Anyway, both are rarely spoken for native Mandarin speakers. You'd better provide more context.