Are you sending lots of mails to a large group of users. If not why not use any normal e-mail service like gmail?

gmail with an app specific password.

A bit overkill but mxroute. Complete own Mail-environment for sending and receiving.

About 50.- a year I think it was

I was using mailgun, but they recently fucked me, so I switched everything to Brevo.

A VPS with Mailcow.

I pay $7 for a noreply user in my business starter Google workspace.

Gmail with app specific password + Postfix docker container loganmarchione/docker-postfixrelay. I configure gmail in one spot (the container) and everything else connects to that container to relay out. You can easily limit destination email addresses with the container as well, so you don’t have to worry about an app going rogue.

Are there any third party services that don't require phone numbers for sign-ups?

Apple mail

I got a Black Friday special at MXRoute a few years ago - $15 for the year.

Host whatever domains you want then for email.

Might get a bargain again this year if they do Black Fridays

Emails? Emails? I don't need no stinkin' emails.

Apologies to treasure of the sierra madres.