fwiw ~ by my read:
Protect your searches with Norton Safe Search reads like notice for Norton Safe Web users that the Norton Safe Web extension will stop providing the ratings to all search engines except for Norton Safe Search.
as to how long you’ll see notice…I’m thinking…for some time…as long as you run Norton Safe Web on Chrome.
I imagine: Norton wants you to run Norton Private Browser.
&
Norton 360 v24 has Browser Protection → Web Shield [here] doesn’t require an extension.