+1 on those services. I went with AWS Cognito, which gives you permanently 50.000 MAU for free. A big issue with self-hosting is also Email delivery; you'd have to go to some provider to send verification Emails to have a decent inboxing rate.
Only downside is the pretty ugly default login UI of cognito, but you can style it to some extend by adding a logo and custom css.
Out sourcing credentials is critical. I'd go a step further, most apps/websites should out-source all of their personal data. Liability around personal data breaches is only increasing.
Only downside is the pretty ugly default login UI of cognito, but you can style it to some extend by adding a logo and custom css.