Posteo is a paid mailbox in Germany, about one euro a month, on electricity they buy as green power. You can pay anonymously. They strip technical headers that would show your IP, they encrypt stored mail, and they will encrypt inbound mail from other providers when they can.
There is no Posteo app. You use IMAP in whatever mail program you already have. The webmail looks old because they spend the money on the mail system. Custom domains are not the point. Aliases exist. It is a quiet address for people who already live in Thunderbird or Apple Mail and do not want a company reading the mail to sell ads.
Use it if you want boring, cheap, German email. posteo.de
Posteo aliases let one quiet address fan out without a custom domain. Turn on the inbound encryption options only after you understand which mail will become unsearchable. IMAP in a mail app is the intended setup. That app can store mail in the clear on the phone. Full-disk encryption and a locked screen still matter. Posteo cannot protect a notification preview on a lock screen.