Even on the latest macOS Sonoma, you can not cut-paste or move files/folders with the Finder's File menu, given that, the cut feature in Finder is designed to cut and paste text instead of files and folders. That's why the Cut button is greyed out when you select a file/folder, you can only allow copy and paste.
While moving files or folders to a different location on your Mac cannot be done directly, there are a few workarounds available:
1. Highlight the desired item, and drag-drop it to the location within Finder.
2. Copy and paste items on Mac and then delete the original items.
3. Relocate the files on Mac using the title bar.
4. Change file location with Terminal commands such as "mv ~/Downloads/MyFile.txt ~/Documents/Work/MyFile.txt."
5. Directly move files to a selected path with iBoysoft MagicMenu's Move To feature in the right-click menu. It will cut the selected item and paste it to the chosen location. With it, you can easily cut-paste files/folders on a Mac.