SQL Server alerts not sending notification emails to the operator
Check SQL Server Agent Properties: on the "Alert System" page, is "Enable mail profile" checked?

Sometimes with new installations, after I set up options on that page I've found notification emails for alerts aren't sent. A restart of the SQL Agent service often addresses that issue for me. - dave-mason

An article that explains more details: How to setup SQL Server alerts and email operator notifications by David Bird - joshua-washburn

Helpful debugging queries: Notes on debugging Database Mail problems by Kenneth Fisher - erik-darling