Hi Duke,
I had this when I connected my M1 MBA to a external monitor for the 1st time. (Under the 1st version of the macOS Big Sur.) The dock stayed on the Laptop screen, but did not appear on the external Monitor.
I played around and got it onto the monitor in the end.
I set the dock to the LHS of the screen. When I moved my cursor to the external monitor, it appeared on the monitor at last, on the LHS. I then set to bottom of screen, and it worked ever after.
Hope that helps. Bit crappy it didn't just work for me, but I got there
Martin