+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.