I have recently upgraded to Big Sur on my iMac. Time Machine doesn't work, Messages doesn't work (to non iPhones), Spotlight takes 10 minutes to do a search and the Adobe programs are glitchy (especially InDesign). When is Apple going to fix it?

Welcome to the Apple Support Communities.

There are no issues with macOS Big Sur.

If you are having issues, I believe we need to proceed with an EtreCheck report. EtreCheck is a useful App to diagnose and identify issues, both hardware and software. It is trusted by many users. Please follow the steps outlined below:

1. Navigate to: https://etrecheck.com and get the free version of EtreCheckPro.
2. Download it. It is a free and trusted app. It is often recommended here on Apple Support Communities. 
3. Open EtreCheck, and before running the report, be sure to check “Allow full Drive Access” at the bottom of the EtreCheckPro window.
4. Run the report, and put it in a post, as seen here: https://discussions.apple.com/docs/DOC-250000211. We will then examine the report for issues in your Mac.

Jack

Haven't experienced any of that with the upgrade. However, Adobe Creative Suite will not function properly on Big Sur, you need to use Adobe Creative Cloud 2021. Learn more: https://helpx.adobe.com/download-install/kb/macos-big-sur.html