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.
My broadband basic info/help site - www.robertos.me.uk.
Domains, site and mail hosting - Tsohost
Connection - AAISP Home::1 80/20. Sync 57825/13835kbps @ 600m. - BQM