Try plugging in the external monitors only on the left side of the Macbook. tested with a $400 Targus thunderbolt Dock210 with two ancient Apple 30" Cinema displays in it; tested with only 1 plugged into the dock, and the other plugged in separately both scenarios work but ONLY when plugged into one of the Mac's LEFT ports. I am using Intel Macbook pro 16" with Big Sur Note that I did not need to install any drivers or software for the docking station.

See my answer at https://developer.apple.com/forums/thread/666645?page=1#679566022 . Basically, plug in both monitors (or dock with 2 monitors) only on the LEFT side of the laptop.

Agreed with @mjrnc, it seems plugging in displays only via the LEFT laptop ports gives the best results. See my full answer regarding 2 external monitors with docking station at https://developer.apple.com/forums/thread/666645?page=1#679566022 .