Cut and Paste in not working in Illustrator 29.7.1 16 bit
I can cut or copy an object but the object will not paste. This problem occurs via the menu and the keyboard shortcut.

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John, when this happens — are the Paste command enabled or disabled in the Edit top menu?
Does anything change if you disable Include SVG Code option in Preferences > Clipboard Handling?
Do you have any third-party clipboard managers? What about Windows Clipboard History (Win+V) — is it on or off?
Can you tell if text is involved or it happens for both text and vector art? -
John Scheers commented
I can cut or copy an object but the app will not paste. This occurs via the menu and keyboard shortcut. Win 11 Home, Version 10.0.26100 Build 26100. Illustrator version 29.7.1.