Logitech Control Center (LCC) will be fully compatible with macOS 11 (Big Sur), but only for a limited period. MacOS 11 (Big Sur) support for Logitech Control Center (LCC) will end early 2021.
If you experience any issues during the limited compatibility period, please make sure that you have LCC version 3.9.11 or later installed. You can download LCC here.
Please note that LCC 3.9.12 does have messages stating that LCC is not compatible with macOS 11 (Big Sur). You can ignore these messages or install LCC 3.9.11 or a newer version to remove the messages.
After the limited compatibility period ends, certain LCC devices will no longer be supported. You can find more information about those devices here. All other LCC devices will work with Logitech Options, which you can download from here.