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. This appears to be affecting both DisplayPort and HDMI displays connected directly and through hubs and adapters.

We saw this issue firsthand after upgrading a MacBook Pro to ‌macOS Big Sur‌ 11.2, with the update preventing an external monitor from connecting with USB-C, and there are several other complaints from affected users.

Upgrading to 11.2 broke my second external monitor connection.
Primary monitor LG Ultrafine 4k (Mac version) connected via Thunderbolt.
Secondary monitor (same model) connected via HDMI->DisplayPort adapter (BENFEI), then DisplayPort->USB-C cable no longer works after updating (worked fine on 11.1 before updating).
macOS appears to recognize the monitor and resolution, as it is shown in display settings, and Apple Support was able to remove into my computer and see both screens. It's almost as if the signal for the monitor to turn on is not being sent.

The second issue results in resolution issues with external displays unable to work at a full 4K 60Hz resolution, instead locked at 30Hz. In some cases, a 4K monitor is only recognized as a 1080p monitor.

It appears that many of those affected with display issues have a 16-inch MacBook Pro, but there are also reports of other Macs with the same connectivity problems. There does not appear to be a reliable, widespread and tested fix or workaround at this time.

Mac users did not experience these problems in the initial release of ‌macOS Big Sur‌ 11.0.1, and it appears that the macOS Big Sur 11.3 update released yesterday also does not address the problem, but there is still some time for Apple to work in a fix before the 11.3 software sees a public release.