CrossOver does not work on the Big Sur, yet. The developer has tested it successfully on several apps using the Big Sur 11.1 beta, so it should be viable soon. I've been keeping an eye on it since I just bought one of the new M1 MacBook Airs, and have a few Windows programs I want to run.
None of this should be considered as hopeful for the iPad. Emulators like CrossOver are mostly prohibited by Apple, and when they are approved they have strong restrictions on how you can load and run apps. Emulators are by their nature are major security concerns on a platform, and Apple is very projective of iOS's security. Yes, this makes some people unhappy. And yes, it makes some people more confident in the security of their iPads. I'm both. Which is why I've gone back to having both a Mac and iPad.