Disconnected from what? Your external display, power - or both? Does it shut down normally if you disconnect the display,, but leave it connected to power? I would suggest that it's the display causing the issue, rather than whether it';s on AC or battery. What display is it? What model MBP is it? You state it's 13", but what's the exact year (click the Apple logo on the menu bar and select 'About this Mac', under the version of macOS you'll see the year and model of your computer).
The nature of your issue points to it being a problem with either the display, the cable - or both. Presumably you're connecting the display via an HDMI cable, yes? There are many here more knowledgeable than I am, but the fact it started after you updated to Big Sur is, to my mind, purely coincidental. If you're connecting via HDMI, does your monitor have the option to connect via Thunderbolt?
Think I'm going to have to defer this to someone more knowledgeable - paging @Grant Bennett-Alder.