Ah, got it!
I too have Cortana disabled so get "Search". What happened is that to get rid of both I right-clicked in their immediate vicinity and was able to disable them.
Right-clicking in the same area gives context menus for File Explorer or the Command Prompt, (next to the Windows one at the left), but right-clicking the Task Bar to the right of my active windows gives the expected menu.
Kindness isn't going to cure the world of all its awfulness but it's a good place to begin. Daisy Ridley.
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