This is very much a regional thing. Working off duty in uniform is unheard of in the NYC/NJ metro area outside large OT events through the Dept like parades. In the south and the west, it’s common.
I’ve seen both. Agency organized details are usually in uniform, though not all uniform gigs are Agency organized. In fact I’ve heard of former LEOs getting arrested here for impersonation because they were working side gigs in their old uniform.
Here we have cops working off duty in uniform at malls, directing traffic at churches, and sitting in their own emergency light equipped cars at road construction.
Various plainclothes security gigs not organized via the Dept are common here as well. There are usually caveats, certain locations like strip clubs are frowned upon or prohibited and pre approval may be required. Guys still work off the books gigs in plainclothes though. Babysitting visiting business men, loss prevention at retail stores etc.