There are several cheap (not free) email providers that allow you to create unique emails per service for this precise purpose, and do not require a phone numbe

There are several cheap (not free) email providers that allow you to create unique emails per service for this precise purpose, and do not require a phone number, however they are lacking significantly in every other way, like an easy to use inbox, so not great for your main contact. One I tested out I found to be good for these random sites that want emails as your username. Then I set the custom email to forward the mail thereby maintaining unique usernames on each site. If the site does not use an email for the username and does not make the provided email public, you could use your regular email with the handy features that come with a Google/Microsoft suite, or air on the side of caution by still having the unique email.