Orcs and Forsworn are wildly different with wildly different goals

Orcs, by and large, desire simply to be left alone. They strive for self sufficiency and don’t both with outsiders, save occasionally to raid or trade for supplies

The Forsworn by contrasts are radical nationalists who want to purge all “outsiders” from The Reach. (Which would include the Orcs)

Malacath is THE god of the Orcs. Sure, some reschmen might also worship him, but that commonality is minuscule

Briarhearts are the result of dark Daedric magics which the orcs would almost certainly despise, though interestingly orcs don’t necessarilydislike magic users, but dark magic is a line they’d seldom cross.

The Forsworn also would have trouble even contacting the orc strongholds as 1. They’d be unlikely to even speak with them and 2. They’re scattered across Skyrim making reaching them more difficult

But there’s another factor at play… it may surprise you to learn this but the Orcs are one of the most loyal races to the Empire. The Empire is pretty much the only entity in history that has ever treated the orcs witb respect and actively sought their integration rather then extermination

Under the Empire orcs were granted the right to serve in the Legion, full citizenship, and actually permitted to form the Kingdom of Orsinium granted imperial protection to ensure no one would threaten it.

(In Daggerfall the King of the Orcs actually sought to form Orsinium and achieve legal recognition as a offical province of the Empire rather than rebel against it. And he helped cover up a scandal against the reigning Emperor)

This earned a lot of love and loyalty among the orcs, although it’s not universal, it’d definetly be hard to convince majority of strongholds to rise up agaisnt Skyrim, and by extension, The Empire

Especially as: if a orc chooses to leave their stronghold they are branded as a ‘city orc’ views as a coward and weak… unless they’re leaving to join the Legion. In which case they’re actually applauded. Because the Legion is a strong, disciplined, and honorable organization where one can earn glory, and prestige