I had this exact problem, and this is what solved it for me. This is what fixed my issue on Big Sur as well. Clear up the desktop - move ALL desktop items away from the edges and corners of the screen. Hide all application windows and close all Finder windows. Reconnect the external monitor. This brings my external monitor back online. I can only surmise that it was caused by some sort of resolution or refresh rate mismatch between my MBP monitor and the external one. Any time anything could potentially be overlapping both displays, this happens when waking up. I hope this works for you too. I'm on Monterey now, and this has brought my external back, but the resolution is still messed up, so that's my next thing to tackle. Good luck!