big sur is not compatible with some cc apps (eg, animate and acrobat) and there are compatible/installable programs that have problems with big sur.
that's said, what problem are you seeing when you try to update?
first try, resetting the cc app: To reset the Creative Cloud desktop app, make sure it's in the foreground, then press:
Win: Ctrl + Alt + R
Mac: Cmd + Opt + R
if that fails, try to repair
if that fails go ahead and uninstall/reinstall per the above link
if that fails, do a clean cc install following each applicable step:
uninstall every cc app including preferences, https://helpx.adobe.com/creative-cloud/help/uninstall-remove-app.html
then uninstall the cc desktop app, https://helpx.adobe.com/creative-cloud/help/uninstall-creative-cloud-desktop-app.html
clean your computer of cc files per http://www.adobe.com/support/contact/cscleanertool.html
check for, and if available, update your os
restart your computer (don't skip this)
reinstall the cc desktop app, https://creative.adobe.com/products/creative-cloud.
if you're unable to install the cc desktop app at this stage, use an administrator account (solution 4 here, https://helpx.adobe.com/creative-cloud/kb/creative-cloud-missing-damaged.html)
use the desktop app to install your cc programs/trials