MacRumors published a story that some users having issues with external displays on macOS Big Sur 11.1 and 11.2.

Some Users Having External Display Connection Issues With macOS Big Sur 11.1 and 11.2

Some macOS Big Sur users who are running the 11.1 and recently released 11.2 update have been experiencing ongoing issues with external displays, based on multiple reports on the MacRumors forum, Apple Support Communities, Twitter, and Reddit. There are at least two separate issues at play, but both are related to external display connections. The problems appear to have started with the ‌macOS Big Sur‌ 11.1 update, and the 11.2 update has not provided a fix and in some cases, has worsened the issue. The first issue causes USB-C ports to fail to recognize external monitors, rendering external displays unusable and unable to connect. 

Some Users Having External Display Connection Issues With macOS Big Sur 11.1 and 11.2