I restarted my browser & the extension I removed came back, & the icon was gone again.
This time when I removed the extension it stayed gone, but so did the icon.
After several browser restarts the extension remains gone, but the icon didn't come back.
I had to remove the Kagi from default everything so that I could remove it from the list of search engines, & re-add it manually yet again. Only then did the icon work again normally.