Probably pulling too much power on battery, you will need to keep it plugged into the mains.
Your MBP should not need to be plugged in to the mains to work with a external display, so something is wrong. First step would be to reset the power management system or SMC
The system management controller (SMC) controls how your Mac manages power. Resetting the SMC can resolve certain issues related to power, battery, fans and other features.support.apple.com
Not sure what is going on, try the SMC reset and let us know if it fixed it.I'm getting a lot of hard crashes on my MacBook Pro M1 as well while attached to an external display. That's with a power source though. In addition the color profile and scaling is often messed up on the monitor when waking the MacBook from sleep. Also getting odd grays and blacks at random in fullscreen apps. Taking them out of fullscreen then back usually resolves it. Very buggy.
I haven't seen a larger discussion regarding the crashing, but I have seen one about the other external display issues. Hopefully a Big Sur patch will come out soon to address these issues.
Not sure what is going on, try the SMC reset and let us know if it fixed it.
On Apple's website it says PRAM reset instructions only apply to Intel Macs. There are 2 SMC reset articles, same instructions however one says only for Intel Macs. Are there another set of instructions you followed for PRAM reset? Also after deleting that file, did it regenerate upon reboot?This morning I reset the PRAM and deleted this file before rebooting:
...and thus far my display weirdness has gone away. At least with DisplayPort. So hopefully this solution sticks.