This has always been the case. Clamshell without power always shut down.
You need a tool like Cafein to keep it open.
The external monitors problems has nothing to do with that. It's a Big Sur problem that started with Catalina, but not that painful.
All older versions than Catalina let you turn the MacbookPro on and immediately close the lid. Then external screens were detected right away and the computer booted to them, showing the Apple logo and then presenting the login screen.
This is not possible anymore.
In Catalina you have to keep the lid open until you have the login prompt. Once you type in the password you can close it. The prompt switches to the monitors.
In Big Sur, this doesn't work, you have to log in with the lid open and wait until it fully boots and shows on all screens before closing the Macbook lid
It's really screwed.
I have two external monitors and I place my Mac underneath them, at the center, using it as a desktop, and it's a pain to keep the lid open and try to see where the boot process is as I don't have room to open it. So i have to pull it out, turn it on, wait for all screen to show the background picture, close it, and then push it back under the screen. We're used to this kind of design non-sense on Windows laptops, not on Macs.